Digital Logic Circuits
1) Given the two binary numbers X = 1010100 and Y = 1000011, perform the subtraction (a) X
-Y and (b) Y - X using 2’s complements.
a) X = 1010100
2’s complement of Y = + 0111101
--------------
Sum = 10010001
Discard end carry
Answer: X - Y = 0010001
b) Y = 1000011
2’s complement of X = + 0101100
---------------
Sum = 1101111
There is no end carry,
Therefore the answer is Y-X = -(2’s complement of 1101111) = -0010001
2). Given the two binary numbers X = 1010100 and Y = 1000011, perform the subtraction (a)
X -Y and (b) Y - X using 1’s complements.
a). X - Y = 1010100 - 1000011
X = 1010100
1’s complement of Y = + 0111100
--------------
Sum = 10010000
End -around carry = + 1
--------------
Answer: X - Y = 0010001
b). Y - X = 1000011 - 1010100
Y = 1000011
1’s complement of X = + 0101011
-----------
Sum = + 1101110
There is no end carry.
Therefore the answer is Y - X = -(1’s complement of 1101110) = -0010001
3). What is meant by parity bit?
A parity bit is an extra bit included with a message to make the total number of 1’s either
even or odd. Consider the following two characters and their even and odd parity:
With even parity With odd parity
ASCII A = 1000001 01000001 11000001
ASCII T = 1010100 11010100 01010100
In each case we add an extra bit in the left most position of the code to produce an even number of
1’s in the character for even parity or an odd number of 1’s in the character for odd parity. The
parity bit is helpful in detecting errors during the transmission of information from one location to
another.
4).What are registers?
register is a group of binary cells. A register with n cells can store any discrete quantity of
information that contains n bits. The state of a register is an n-tuple number of 1’s and 0’s, with
each bit designating the state of one cell in the register.
5). What is meant by register transfer?
A register transfer operation is a basic operation in digital systems. It consists of transfer of
binary information from one set of registers into another set of registers. The transfer may be direct
from one register to another, or may pass through data processing circuits to perform an operation.
6). Define binary logic?
Binary logic consists of binary variables and logical operations. The variables are
designated by the alphabets such as A, B, C, x, y, z, etc., with each variable having only two
distinct values: 1 and 0. There are three basic logic operations: AND, OR, and NOT.
7). Define logic gates?
Logic gates are electronic circuits that operate on one or more input signals to produce an
output signal. Electrical signals such as voltages or currents exist throughout a digital system in
either of two recognizable values. Voltage- operated circuits respond to two separate voltage levels
that represent a binary variable equal to logic 1 or logic 0.
8).Define duality property.
Duality property states that every algebraic expression deducible from the postulates of
Boolean algebra remains valid if the operators and identity elements are interchanged. If the dual
of an algebraic expression is desired, we simply interchange OR and AND operators and replace
1’s by 0’s and 0’s by 1’s.
9).Find the complement of the functions F1 = x’yz’ + x’y’z and F2 = x(y’z’ + yz). By applying
De Morgan’s theorem as many times as necessary.
F1’ = (x’yz’ + x’y’z)’ = (x’yz’)’(x’y’z)’ = (x + y’ + z)(x + y +z’)
F2’ = [x(y’z’ + yz)]’ = x’ + (y’z’ + yz)’
= x’ + (y’z’)’(yz)’
= x’ + (y + z)(y’ + z’)
10).Find the complements of the functions F1 = x’yz’ + x’y’z and F2 = x(y’z’ + yz). by taking
their duals and complementing each literal.
F1 = x’yz’ + x’y’z
The dual of F1 is (x’ + y + z’)(x’ + y’ + z)
Complementing each literal: (x + y’ + z)(x + y + z’)
F2 = x(y’z’ + yz).
The dual of F2 is x + (y’ + z’)(y + z).
Complement of each literal: x’ + (y + z)(y’ + z’)
11).State De Morgan’s theorem.
De Morgan suggested two theorems that form important part of Boolean algebra. They are,
1) The complement of a product is equal to the sum of the complements.
(AB)’ = A’ + B’
2) The complement of a sum term is equal to the product of the complements.
(A + B)’ = A’B’
12).Reduce A.A’C
A.A’C = 0.c [A.A’ = 1]
= 0
13). Reduce A(A + B)
A(A + B) = AA + AB
= A(1 + B) [1 + B = 1]
= A.
14. Reduce A’B’C’ + A’BC’ + A’BC
A’B’C’ + A’BC’ + A’BC = A’C’(B’ + B) + A’B’C
= A’C’ + A’BC [A + A’ = 1]
= A’(C’ + BC) = A’(C’ + B) [A + A’B = A + B]
15.) Reduce AB + (AC)’ + AB’C(AB + C)
AB + (AC)’ + AB’C(AB + C) = AB + (AC)’ + AAB’BC + AB’CC
= AB + (AC)’ + AB’CC [A.A’ = 0]
= AB + (AC)’ + AB’C [A.A = 1]
= AB + A’ + C’ =AB’C [(AB)’ = A’ + B’]
= A’ + B + C’ + AB’C [A + AB’ = A + B]
= A’ + B’C + B + C’ [A + A’B = A + B]
= A’ + B + C’ + B’C
=A’ + B + C’ + B’
=A’ + C’ + 1
= 1 [A + 1 =1]
16. Simplify the following expression Y = (A + B)(A + C’ )(B’ + C’ )
Y = (A + B)(A + C’ )(B’ + C’ )
= (AA’ + AC +A’B +BC )(B’ + C’) [A.A’ = 0]
= (AC + A’B + BC)(B’ + C’ )
= AB’C + ACC’ + A’BB’ + A’BC’ + BB’C + BCC’
= AB’C + A’BC’
17).Simplify the following using De Morgan’s theorem [((AB)’C)’’ D]’
[((AB)’C)’’ D]’ = ((AB)’C)’’ + D’ [(AB)’ = A’ + B’]
= (AB)’ C + D’
= (A’ + B’ )C + D’
18.Show that (X + Y’ + XY)( X + Y’)(X’Y) = 0
(X + Y’ + XY)( X + Y’)(X’Y) = (X + Y’ + X)(X + Y’ )(X’ + Y) [A + A’B = A + B]
= (X + Y’ )(X + Y’ )(X’Y) [A + A = 1]
= (X + Y’ )(X’Y) [A.A = 1]
= X.X’ + Y’.X’.Y
= 0 [A.A’ = 0]
19).Prove that ABC + ABC’ + AB’C + A’BC = AB + AC + BC
ABC + ABC’ + AB’C + A’BC =AB(C + C’) + AB’C + A’BC
=AB + AB’C + A’BC
=A(B + B’C) + A’BC
=A(B + C) + A’BC
=AB + AC + A’BC
=B(A + C) + AC
=AB + BC + AC
=AB + AC +BC ...Proved
20).Convert the given expression in canonical SOP form Y = AC + AB + BC
Y = AC + AB + BC
=AC(B + B’ ) + AB(C + C’ ) + (A + A’)BC
=ABC + ABC’ + AB’C + AB’C’ + ABC + ABC’ + ABC
=ABC + ABC’ +AB’C + AB’C’ [A + A =1]
21).Convert the given expression in canonical POS form Y = ( A + B)(B + C)(A + C)
Y = ( A + B)(B + C)(A + C)
= (A + B + C.C’ )(B + C + A.A’ )(A + B.B’ + C)
= (A + B + C)(A + B + C’ )(A + B +C)(A’ + B +C)(A + B + C)(A + B’ + C) [A + BC
= (A + B)(A + C)
Distributive law]
= (A + B + C)(A + B + C’)(A’ + B + C)(A’ + B + C)(A + B’ + C)
22). Find the minterms of the logical expression Y = A’B’C’ + A’B’C + A’BC + ABC’
Y = A’B’C’ + A’B’C + A’BC + ABC’
=m0 + m1 +m3 +m6
=™P
23).Write the maxterms corresponding to the logical expression Y = (A + B + C’ )(A + B’ +
C’)(A’ + B’ + C)
Y = (A + B + C’ )(A + B’ + C’)(A’ + B’ + C)
=M1.M3.M6
=š0
24).Convert (4021.2)5 to its equivalent decimal.
(4021.2)5 = 4 x 53 + 0 x 52 + 2 x 51 + 1 x 50 + 2 x 5-1
= (511.4)10
25) Using 10’s complement subtract 72532 - 3250
M = 72532
10’s complement of N = + 96750
-----------
Sum = 169282
Discard end carry
Answer = 69282
26) What are called don’t care conditions?
In some logic circuits certain input conditions never occur, therefore the corresponding output
never appears. In such cases the output level is not defined, it can be either high or low. These
output levels are indicated by ‘X’ or‘d’ in the truth tables and are called don’t care conditions or
incompletely specified functions.
27) Write down the steps in implementing a Boolean function with levels of NAND Gates?
Simplify the function and express it in sum of products.
Draw a NAND gate for each product term of the expression that has at least two literals.
The inputs to each NAND gate are the literals of the term. This constitutes a group of first
level gates. Draw a single gate using the AND-invert or the invert-OR graphic symbol in
the second level, with inputs coming from outputs of first level gates.
A term with a single literal requires an inverter in the first level. How ever if the single literal
is complemented, it can be connected directly to an input of the second level NAND gate.
28) Give the general procedure for converting a Boolean expression in to multilevel NAND
diagram?
Draw the AND-OR diagram of the Boolean expression.
Convert all AND gates to NAND gates with AND-invert graphic symbols.
Convert all OR gates to NAND gates with invert-OR graphic symbols.
Check all the bubbles in the same diagram. For every bubble that is not compensated by
another circle along the same line, insert an inverter or complement the input literal.
29) What are combinational circuits?
A combinational circuit consists of logic gates whose outputs at any time are determined
from the present combination of inputs. A combinational circuit performs an operation that can be
specified logically by a set of Boolean functions. It consists of input variables, logic gates, and
output variables.
30) Give the design procedures for the designing of a combinational circuit.
The procedure involves the following steps,
From the specification of the circuit, determine the required number of inputs and outputs and
assign a symbol to each.
Derive the truth table that defines the required relationships between inputs and outputs.
Obtain the simplified Boolean functions for each output as a function of the input variables.
Draw the logic diagram and verify the correctness of the design.
31) Define half adder.
A combinational circuit that performs the addition of two bits is called a half adder. A half
adder needs two binary inputs and two binary outputs. The input variables designate the augend
and addend bits; the output variables produce the sum and carry
32) Define full adder?
A combinational circuit that performs the adtion of three bits is a full adder.It consists of
three inputs and two outputs.
33) Define binary adder.
A binary adder is a digital circuit that produces the arithmetic sum of two binary numbers. It
can be constructed with full adders constructed in cascade, with the output carry from each full
adder connected to the input carry of the next full adder in the chain.
34) What is overflow?
Over flow is a problem in digital computers because the number of bits that hold the
number is finite and a result that contains n + 1 bits cannot be accommodated. For this reason
many computers detect the occurrence of an overflow, and when it occurs a corresponding flip flop
is set that can be checked by the user. An overflow condition can be detected by observing the
carry into sign bit position and the carry out of the sign bit position. If these two carries are not
equal, an overflow has occurred.
35) Define magnitude comparator?
A magnitude comparator is a combinational circuit that compares two numbers, A and B,
and determines their relative magnitudes. The outcome of the comparison is specified by three
binary variables that indicate whether a>b, A = b, or A < B.
36) What are decoders?
A decoder is a combinational circuit that converts binary information from n input lines to a
maximum of 2n unique output lines. If the n bit coded information has unused combinations, he
decoder may have fewer than 2n outputs.
37) What are encoders?
An encoder is a digital circuit that performs the inverse operation of a decoder. An encoder
has 2n and n output lines. The output lines generate the binary code corresponding to the input
value.
38) Define priority encoder?
A priority encoder is an encoder circuit that includes the priority function. The operation of
priority encoder is such that if two or more inputs are equal to 1 at the same time, the input having
the highest priority will take precedence.
39) Define multiplexer?
A multiplexer is combinational circuit that selects binary information from one of many input
lines and directs it to a single output line. The selection of a particular input line is controlled by a
set of selection lines. Normally there are 2n input lines and n selection lines whose bit combinations
determine which input is selected.
40) Define binary decoder?
A decoder which has an n- bit binary input code and a one activated output out-of -2n
output code is called binary decoder. A binary decoder is used when it is necessary to activate
exactly one of 2n outputs based on an n-bit input value.
41. Represent binary number 1101 - 101 in power of 2 and find its decimal equivalent
N = 1 x 2 3 + 1 x 2 2 + 0 x 2 1 + 1 x 2 0 + 1 x 2 -1 + 0 x 2 -2 + 1 x 2 -3
= 13.625 10
42. Convert (634) 8 to binary
6 3 4
110 011 100
Ans = 110 011 100
43. Convert (9 B 2 - 1A) H to its decimal equivalent.
N = 9 x 16 2 + B x 16 1 + 2 x 16 0 + 1 x 16 -1 + A (10) x 16 -2
= 2304 + 176 + 2 + 0.0625 + 0.039
= 2482.1 10
44. What are the different classification of binary codes?
1. Weighted codes
2. Non - weighted codes
3. Reflective codes
. Sequential codes
5. Alphanumeric codes
6. Error Detecting and correcting codes.
45. Convert 0.640625 decimal number to its octal equivalent.
0.640625 x 8 = 5.125
0.125 x 8 = 1.0
Ans. = 0.640 625 10 = 0.51
46. Convert 0.1289062 decimal number to its hex equivalent
0.1289062 x 16 = 2.0625
0.0625 x 16 = 1.0
Ans. = 0.21 16
47. Convert decimal number 22.64 to hexadecimal number.
16 22 -6
16 1 -1
0
0.64 x 16 = 10.24
0.24 x 16 = 3.84
0.84 x 16 = 13.44
.44 x 16 = 7.04
Ans. = (16 . A 3 D 7) 16.3
48. What are the two steps in Gray to binary conversion?
The MSB of the binary number is the same as the MSB of the gray code number.
So write it down.To obtain the next binary digit, perform an exclusive OR operation
b/n the bit just written down and the next gray code bit. Write down the result.
49. Convert gray code 101011 into its binary equivalent.
Gray Code : 1 0 1 0 1 1
Binary Code 1 1 0 0 1 0
50. Convert 10111011 is binary into its equivalent gray code.
Binary Code: 1 0 1 1 1 0 1 0 1 1
Gray code : 1 1 1 0 0 1 1 0
1 0 1 0
0 0 1 1
1 1 0 1
52. Substract (0 1 0 1) 2 from (1 0 1 1) 2
1 0 1 0
0 1 0 1
0 1 1 0
53. Find 2’S complement of (1 0 1 0 0 0 1 1) 2
0 1 0 1 1 1 0 0 1 1’s Complement
+ 0 0 0 0 0 0 0 1
0 1 0 1 1 1 0 1 0 2’s complement.
54. Substract 1 1 1 0 0 1 2 from 1 0 1 0 1 1 2 using 2’s complement method
1 0 1 0 1 1
+ 0 0 0 1 1 1 2’s comp. of 1 1 1 0 0 1
1 1 0 0 1 0 Ans. in 2’s complement form
- 0 0 1 1 1 0 Answer in true form.
55. What are the advantages of 1’s complement subtraction?
1) The 1’s complement subtraction can be accomplished with an binary adder.
Therefore, this method is useful in arithmetic logic circuits.
2) The is complement of a number is easily obtained by inverting each bit in the
number
56. Find the excess -3 code and 9’s complement of the number 403 10
4 0 3
0 1 0 0 0 0 0 0 0 0 1 1
0 0 1 1 0 0 1 1 0 0 1 1 +
0 1 1 1 0 0 1 1 0 1 1 0 excess 3 code
9’s complement 1 0 0 0 1 1 0 0 1 0 0 1
57. Write the names of basic logical operators.
1. NOT / INVERT
2. AND
3. OR
58. Simplify the following expression
y = (A + B) (A = C) (B + C)
= (A A + A C + A B + B C) (B + C)
= (A C + A B + B C) (B + C)
= A B C + A C C + A B B + A B C + B B C + B C C
= A B C = A B C
59. Show that the NAND connection is not associative
The NAND connection is not associative says that
A . B . C A . B. C
A . B + C A + B C
AB + C A + BC
60. What is a Logic gate?
Logic gates are the basic elements that make up a digital system. The electronic gate is a
circuit that is able to operate on a number of binary inputs in order to perform a particular
logical function.
61. Write the names of Universal gates.
1. NAND gate
2. NOR gate
62. Why are NAND and NOR gates known as universal gates?
The NAND and NOR gates are known as universal gates, since any logic function
can be implemented using NAND or NOR gates.
63. Define combinational logic
When logic gates are connected together to produce a specified output for certain
specified combinations of input variables, with no storage involved, the resulting
circuit is called combinational logic.
64. Explain the design procedure for combinational circuits
¢ The problem definition
¢ The determination of number of available input variables & required O/P
variables.
¢ Assigning letter symbols to I/O variables
¢ Obtain simplified boolean expression for each O/P.
¢ Obtain the logic diagram.
65. Define half adder and full adder
The logic circuit which performs the addition of two bits is a half adder.
The circuit which performs the addition of three bits is a full adder.
66. Define Decoder?
A decoder is a multiple - input multiple output logic circuit which converts coded
inputs into coded outputs where the input and output codes are different.
67. What is binary decoder?
A decoder which has an n-bit binary i/p code and a one activated output out of 2l.
output code is called binary decoder. It is used when it is necessary to activate
exactly one of 2 n out puts based on an n - bit input value.
68. Define Encoder?
An encoder has 2n input lines and n output lines. In encoder the output lines generate
the binary code corresponding to the input value.
69. What is priority Encoder?
A priority encoder is an encoder circuit that includes the priority function. In priority encoder, if 2 or
more inputs are equal to 1 at the same time, the input having the highest priority will take
precedence.
70. Define multiplexer?
Multiplexer is a digital switch. If allows digital information from several sources to
be routed onto a single output line.
71. What do you mean by comparator
A comparator is a special combinational circuit designed primarily to compare the
relative magnitude of two binary numbers.
72. List basic types of programmable logic devices.
1. Read only memory
2. Programmable logic Array
3. Programmable Array Logic
73. Define ROM
A read only memory is a device that includes both the decoder and the OR gates
within a single IC package.
74. Define address and word:
In a ROM, each bit combination of the input variable is called on address. Each bit
combination that comes out of the output lines is called a word.
75. What are the types of ROM
1. Masked ROM.
2. Programmable Read only Memory
3. Erasable Programmable Read only memory.
4. Electrically Erasable Programmable Read only Memory.
76. What is programmable logic array? How it differs from ROM?
In some cases the number of don™t care conditions is excessive, it is more economical to use a
second type of LSI component called a PLA
A PLA is similar to a ROM in concept; however it does not provide full decoding of the variables
and does not generates all the minterms as in the ROM..12
77. What is mask - programmable?
With a mask programmable PLA, the user must submit a PLA PLA program table to the
manufacturer.
78. What is field programmable logic array?
The second type of PLA is called a field programmable logic array. The EPLA can
be programmed by the user by means of certain recommended procedures.
79. Give the comparison between prom and PLA.
PROM PLA
1. And array is fixed and or Both AND and OR arrays are
array is programmable. Programmable.
2. Cheaper and simple to use. Costliest and complex than PROMS.
80. Define even parity
In even parity the added parity bit will make the total number of 1s an even amount.
81. Define sequential circuit?
In sequential circuits the output variables dependent not only on the present input
variables but they also depend up on the past history of these input variables.
82. Give the comparison between combinational circuits and sequential circuits.
Memory unit is not required Memory unity is required
Parallel adder is a combinational circuit Serial adder is a sequential circuit
83. What do you mean by present state?
The information stored in the memory elements at any given time define™s the present state of the
sequential circuit.
84. What do you mean by next state?
The present state and the external inputs determine the outputs and the next state of the
sequential circuit.
85. What are the types of sequential circuits?
1. Synchronous sequential circuits
2. Asynchronous sequential circuits
86. Define synchronous sequential circuit
In synchronous sequential circuits, signals can affect the memory elements only at
discrete instant of time.
87. Define Asynchronous sequential circuit?
In asynchronous sequential circuits change in input signals can affect memory element at any
instant of time
88. Define flip-flop
Flip - flop is a sequential device that normally. samples its inputs and changes its
outputs only at times determined by clocking signal.
89. List various types of flip-flop
1] S.R. latch
2] D latch
3] Clocked J.K. flip-flop
4] T flip-flop
90. What is race around condition?
In the JK latch, the output is feedback to the input, and therefore change in the
output results change in the input. Due to this in the positive half of the clock pulse
if J and K are both high then output toggles continuously. This condition is known
as race around condition.
91. Define rise time and fall time?
The time required to change the voltage level from 10% to 90% is known as rise
time, and the time required to change the voltage level from 90% to 10% is known
as fall time.
92. Define propagation Delay?
A propagation delay is the time required to change the output after application of the input.
93. Define shift Registers
The binary information in a register can be moved from stage to stage within the
register or into or out of the register upon application of clock pulses. This type of
bit movement or shifting is essential for certain arithmetic and logic operations used
in microprocessors.
This gives rise to a group of registers called shift registers.
94. What are the types of shift register?
1. Serial in serial out shift register?
2. Serial in parallel out shift register
3. Parallel in serial out shift register
4. Parallel in parallel out shift register
5. Bidirectional shift register shift register.
95. What are the types of counter?
1. Synchronous counter
2. Asynchronous Counter
96. What are the two models in synchronous sequential circuits.
1. Moore circuit
2. Mealy circuit
97. What is moore circuit?
When the output of the sequential circuit depends only on the present state of the
flip-flop, the sequential circuit is referred to as moore circuit.
98. What is Mealy circuit?
When the output of the sequential circuit depends on both the present state of flipflop
and on the input, the sequential circuit is referred to as mealy circuit.
99. Define successor
In a state diagram, if an input sequence, x takes a machine from state si to state sj,
then sj is said to be the x - successor of si.
100. Define strongly connected machine?
In a sequential machine many times certain subsets of states may not be reachable
from other subsets of states, even if the machine does not contain any terminal state.
However, if for every pair of states si, sj of a sequential machine, there eights an
input sequence which takes M from Si to Sj then sequential machine M is said to be
strongly connected.
Thursday, September 23, 2010
Quick revision for Electromagnetism
1.State stokes theorem.
The line integral of a vector around a closed path is equal to the surface integral of the normal component of its curl over any surface bounded by the path
H.dl = (ÑxH)ds
2.State coulombs law.
Coulombs law states that the force between any two point charges is directly
proportional to the product of their magnitudes and inversely proportional to the square
of the distance between them. It is directed along the line joining the two charges.
F=Q1Q2 / 4ðår2 ar
3.State Gauss law for electric fields
The total electric flux passing through any closed surface is equal to the total charge enclosed by that surface.
4.Define electric flux.
The lines of electric force is electric flux.
5.Define electric flux density.
Electric flux density is defined as electric flux per unit area.
6.Define electric field intensity.
Electric field intensity is defined as the electric force per unit positive charge.
E =F/ Q =Q/4ðår2 V/m
Electro Magnetic Theory
7.Name few applications of Gauss law in electrostatics.
Gauss law is applied to find the electric field intensity from a closed surface.e.g)Electric field can be determined for shell, two concentric shell or cylinders etc.
8.What is a point charge?
Point charge is one whose maximum dimension is very small in comparison with any
other length.
9.Define linear charge density.
It is the charge per unit length.
10.Write poisson’s and laplace ’s equations.
Poisson ‘s eqn:
Ñ2V= - ñv / å
Laplace’ s eqn:
Ñ2V= 0
11.State the condition for the vector F to be solenoidal.
Ñ·F =0
12. .State the condition for the vector F to be irrotational.
ÑxF =0
13.Define potential difference.
Potential difference is defined as the work done in moving a unit positive charge
from one point to another point in an electric field.
14.Define potential.
Potential at any point is defined as the work done in moving a unit positive charge
from infinity to that point in an electric field.
V=Q / 4ðår
15.Give the relation between electric field intensity and electric flux density.
D=åE C/m2
16.Give the relationship between potential gradiant and electric field.
E= - ÑV
17.What is the physical significance of div D ?
Ñ·D=-ñv
The divergence of a vector flux density is electric flux per unit volume leaving a small volume. This is equal to the volume charge density.
18. Define current density.
Current density is defined as the current per unit area.
J= I/A Amp/m2
19.Write the point form of continuity equation and explain its significance.
Ñ·J= - ñv / t
20.Write the expression for energy density in electrostatic field.
W=1 / 2 åE2
21.Write the boundary conditions at the interface between two perfect dielectrics.
i)The tangential component of electric field is continuous i.e)Et1=Et2
ii)The normal component of electric flux density is continuous I.e)Dn1=Dn2
22.Write down the expression for capacitance between two parallel plates.
C=åA / d
23.What is meant by displacement current?
Displacement current is nothing but the current flowing through capacitor.
J= D / t
24.State point form of ohms law.
Point form of ohms law states that the field strength within a conductor is
proportional to the current density.J=óE
25 Define surface charge density.
It is the charge per surface area.
26.State amperes circuital law.
Magnetic field intensity around a closed path is equal to the current enclosed by the
path. H·dl=I
27.State Biot –Savarts law.
It states that the magnetic flux density at any point due to current element is
proportional to the current element and sine of the angle between the elemental length
and inversely proportional to the square of the distance between them
dB=μ 0Idl sinè / 4ðr2
28.Define magnetic vector potential.
It is defined as that quantity whose curl gives the magnetic flux density.
B=Ñ x A =μ / 4ð J/r dv web/m2
29.Write down the expression for magnetic field at the centre of the circular coil.
H = I/2a.
30.Give the relation between magnetic flux density and magnetic field intensity.
B =μ H
31.Write down the magnetic boundary conditions.
i) The normal components of flux density B is continuous across the boundary.
ii) The tangential component of field intensity is continuous across the boundary.
32.Give the force on a current element.
dF = BIdlsinè
33..Define magnetic moment.
Magnetic moment is defined as the maximum torque per magnetic induction of
flux density. m=IA
34.State Gauss law for magnetic field.
The total magnetic flux passing through any closed surface is equal to zero.
B.ds =0
35.Define a wave.
If a physical phenomenon that occurs at one place at a given time is reproduced at
other places at later times , the time delay being proportional to the space separation
from the first location then the group of phenomena constitutes a wave.
36. Mention the properties of uniform plane wave.
i) At every point in space ,the electric field E and magnetic field H are perpendicular to each other.
ii)The fields vary harmonically with time and at the same frequency everywhere in
space.
37.Write down the wave equation for E and H in free space.
Ñ2H– μ 0å0
2H / t 2 =0.
38.Define intrinsic impedance or characteristic impedance.
It is the ratio of electric field to magnetic field.or It is the ratio of square root of permeability to permittivity of medium.
39.Give the characteristic impedance of free space.
377ohms
40.Define propagation constant.
Propagation constant is a complex number
ã =á +jâ
where á is attenuation constant
â is phase constant
ã = jùμ (ó +jùå)
41.Define skin depth
It is defined as that depth in which the wave has been attenuated to 1/e or
approximately 37% of its original value.
Ä = 1/á = 2 / jùó
42.Define Poynting vector.
The poynting vector is defined as rate of flow of energy of a wave as it propagates.
P =E X H
43. State Poyntings Theorem.
The net power flowing out of a given volume is equal to the time rate of decrease
of the the energy stored within the volume- conduction losses.
44.Give significant physical difference between poisons and laplaces equations.
When the region contains charges poisons equation is used and when
there is no charges laplaces equation is applied.
45.Give the difficulties in FDM.
FDM is difficult to apply for problems involving irregular boundaries and non
homogenious material properties.
46.Explain the steps in finite element method.
i) Discretisation of the solution region into elements.
ii) Generation of equations for fields at each element
iii) Assembly of all elements
iv) Solution of the resulting system
47.State Maxwells fourth equation.
The net magnetic flux emerging through any closed surface is zero.
48. State Maxwells Third equation
The total electric displacement through the surface enclosing a volume is equal to the total charge within the volume.
49.State the principle of superposition of fields.
The total electric field at a point is the algebraic sum of the individual electric field at that point.
50.Define ohms law at a point
Ohms law at appoint states that the field strength within a conductor is proportional
to current density.
51.Define self inductance.
Self inductance is defined as the rate of total magnetic flux linkage to the current
through the coil.
52.Define pointing vector.
The vector product of electric field intensity and magnetic field intensity at a point is a measure of the rate of energy flow per unit area at that point.
53.Give the formula to find potential at a point which is surrounded by four
orthogonal points in FDM.
V0= ¼(V1+V2+V3+V4)
54.Give the formula to find potential at a point which is surrounded by six
orthogonal points in FDM.
V0= ¼(V1+V2+V3+V4 +V5+V6)
55.State Lenz law.
Lenz’s law states that the induced emf in a circuit produces a current which opposes the change in magnetic flux producing it.
56.What is the effect of permittivity on the force between two charges?
Increase in permittivity of the medium tends to decrease the force between two
charges and decrease in permittivity of the medium tends to increase the force between
two charges.
57.State electric displacement.
The electric flux or electric displacement through a closed surface is equal to the charge enclosed by the surface.
58.What is displacement flux density?
The electric displacement per unit area is known as electric displacement density or
electric flux density.
59.What is the significance of displacement current?
The concept of displacement current was introduced to justify the production of
magnetic field in empty space. It signifies that a changing electric field induces a
magnetic field .In empty space the conduction current is zero and the magnetic fields are entirely due to displacement current.
60.Distinguish between conduction and displacement currents.
The current through a resistive element is termed as conduction current whereas the
current through a capacitive element is termed as displacement current.
61.Define magnetic field strength.
The magnetic field strength (H) is a vector having the same direction as magnetic flux
density.
H=B/μ
62.Give the formula to find the force between two parallel current carrying
conductors.
F=μI I1 / 2ðR
63.Give the expression for torque experienced by a current carrying loop situated in
a magnetic field.
T = IABsinè
64 What is torque on a solenoid?
T = NIABsinè
65.Explain the conservative property of electric field.
The work done in moving a point charge around a closed path in a electric field is zero. Such a field is said to be conservative.
E.dl = 0
66.Write he expression for field intensity due to a toroid carrying a filamentary
current ?
I H=NI / 2ïR
67.What are equipotential surfaces?
An equipotential surface is a surface in which the potential energy at every point is of the same vale.
68.Define loss tangent.
Loss tangent is the ratio of the magnitude of conduction current density to displacement current density of the medium.
Tan ä = ó / ùå
69.Defie reflection and transmission coefficients.
Reflection coefficient is defined as the ratio of the magnitude of the reflected field to that of the incident field.
70. Define transmission coefficients.
Transmission coefficient is defined as the ratio of the magnitude of the
transmitted field to that of incident field.
71.What will happen when the wave is incident obliquely over dielectric –dielectric
boundary?
When a plane wave is incident obliquely on the surface of a perfect dielectric part of the energy is transmitted and part of it is reflected .But in this case the transmitted wave will be refracted, that is the direction of propagation is altered.
72.What is the expression for energy stored in a magnetic field?
W = ½ LI2
73.What is energy density in magnetic field?
W = ½ μH2
74.Distinguish between solenoid and toroid.
Solenoid is a cylindrically shaped coil consisting of a large number of closely spaced turns of insulated wire wound usually on a non magnetic frame.
If a long slender solenoid is bent into the form of a ring and there by closed on itself it becomes a toroid.
75.Describe what are the sources of electric field and magnetic field?
Stationary charges produce electric field that are constant in time, hence the term
electrostatics. Moving charges produce magnetic fields hence the term magnetostatics.
76.What are the significant physical differences between Poisson ‘s and laplace ‘s
equations.
Poisson ‘s and laplace ‘s equations are useful for determining the electrostatic potential V in regions whose boundaries are known. When the region of interest contains charges poissons equation can be used to find the
potential.
When the region is free from charge laplace equation is used to find the potential.
77.State Divergence Theorem.
The integral of the divergence of a vector over a volume v is equal to the surface integral of the normal component of the vector over the surface bounded by the volume.
78.Give the expression for electric field intensity due to a single shell of charge
E = Q / 4ðår2
79.Give the expression for potential between two spherical shells
V= 1/ 4ð (Q1/a – Q2/b)
80.Define electric dipole.
Electric dipole is nothing but two equal and opposite point charges separated by a finite distance.
81.What is electrostatic force?
The force between any two particles due to existing charges is known as electrostatic
force, repulsive for like and attractive for unlike.
82.Define divergence.
The divergence of a vector F at any point is defined as the limit of its surface integral per unit volume as the volume enclosed by the surface around the point shrinks to zero.
83.How is electric energy stored in a capacitor?
In a capacitor, the work done in charging a capacitor is stored in the form of electric
energy.
84.What are dielectrics?
Dielectrics are materials that may not conduct electricity through it but on applying electric field induced charges are produced on its faces .The valence electron in atoms of a dielectric are tightly bound to their nucleus.
85.What is a capacitor?
A capacitor is an electrical device composed of two conductors which are separated
through a dielectric medium and which can store equal and opposite charges ,independent
of whether other conductors in the system are charged or not.
86.Define dielectric strength.
The dielectric strength of a dielectric is defined as the maximum value of electric field that can b applied to the dielectric without its electric breakdown.
87.What meaning would you give to the capacitance of a single conductor?
A single conductor also possess capacitance. It is a capacitor whose one plate is at
infinity.
88.Why water has much greater dielectric constant than mica.?
Water has a much greater dielectric constant than mica .because water ha a permanent
dipole moment, while mica does not have.
89.What is lorentz force?
Lorentz force is the force experienced by the test charge .It is maximum if the direction of movement of charge is perpendicular to the orientation of field lines.
90.Define magnetic moment.
Magnetic moment is defined as the maximum torque on the loop per unit magnetic
induction.
91.Define inductance.
The inductance of a conductor is defined as the ratio of the linking magnetic flux to the current producing the flux. L = NÔ / I
92.What is main cause of eddy current?
The main cause of eddy current is that it produces ohmic power loss and causes local
heating.
93.How can the eddy current losses be eliminated?
The eddy current losses can be eliminated by providing laminations. It can be proved
that the total eddy current power loss decreases as the number of laminations increases.
94.What is the fundamental difference between static electric and magnetic field
lines?
There is a fundamental difference between static electric and magnetic field lines .The tubes of electric flux originate and terminates on charges, whereas magnetic flux tubes are continuous.
95.What are uniform plane waves?
Electromagnetic waves which consist of electric and magnetic fields that are
perpendicular to each other and to the direction of propagation and are uniform in plane
perpendicular to the direction of propagation are known as uniform plane waves.
96.Write short notes on imperfect dielectrics.
A material is classified as an imperfect dielectrics for ó <<ùå, that is conduction current
density is small in magnitude compared to the displacement current density.
97.What is the significant feature of wave propagation in an imperfect dielectric ?
The only significant feature of wave propagation in an imperfect dielectric compared to
that in a perfect dielectric is the attenuation undergone by the wave.
98.What is the major drawback of finite difference method?
The major drawback of finite difference method is its inability to handle curved
boundaries accurately.
99.What is method of images?
The replacement of the actual problem with boundaries by an enlarged region or with
image charges but no boundaries is called the method of images.
100.When is method of images used?
Method of images is used in solving problems of one or more point charges in the
presence of boundary surfaces.
Part-B
1.Find the electric field intensity of a straight uniformly charged wire of length ‘L’m
and having a linear charge density of +ë C/m at any point at a distance of ‘h’ m.
Hence deduce the expression for infinitely long conductor.
Hints: Field due to charge element is given by:
dE = ëdi/ 4ðîr2
Ex=ë [cos á1+cosá2] /4ðåh
Ey=ë [sin á1-siná2] /4ðåh
For infinitely long conductor
E = ël / 4ðåh
2.Derive the boundary relations for electric fields.
Hints:
i)The tangential component of the electric field is continuous at the surface
.Et1 = Et2
ii)The normal component of the electric flux density is continuous if there is no surface
charge density.
Dn1 = Dn2
3.Find the electric field intensity produced by a point charge distribution at
P(1,1,1)caused by four identical 3nC point charges located at P1(1,1,0)
P2(-1,1,0) P3(-1,-1,0) and P4(1,-1,0).
Hints:
Find the field intensity at P by using the formula
Ep = 1/4åð[( Q1/r1p
2 u1p ) +(q2/r2p
2 u2p) +(q3/r3p
2 u3p)+(q4/r4p
2)u4p)]
4.A circular disc of radius ‘a’ m is charged with a charge density of óC/m2 .Find the
electric field intensity at a point ‘h’m from the disc along its axis.
Hints:
Find the field due to the tangential and normal components
Total field is given by
E =ñs /2å [1-cos á]
5. Four positive charges of 10–9 C each are situated in the XY plane at points
(0,0) (0,1) (1,0) and (1,1).Find the electric field intensity and potential at
(1/2 ,1/2).
Hints:
Find the field intensity at point using the formula
E = Q / 4ðår2 ur
Find the potential at point using the formula
V = Q / 4ðår
Find the field intensity at the point due to all four charges by using the superposition
principle.
6. Given a electric field E = (-6y/x2) x + 6/x y + 5 z .Find the potential difference VAB
given A(-7,2,1) and B( 4,1,2)
Hint:
Find the potential using the formula v=-/E.dl and substitute the points
7.Derive an expression for potential difference between two points in an electric
field.
Hint:
The potential difference between two points r1 and r2 is
V = V1 –V2
V = Q / 4ðår1 _ Q / 4ðår 2
8.Find the magnetic flux density at a point Z on the axis of a circular loop of radius ‘a’ that carries a direct current I.
Hints:
The magnetic flux density at a point due to the current element is given by
dB = μIdl / 4ð r2
B = μIa2 / 2(a2 + z2)3/2
9.Determine the force per meter length between two long parallel wires A and B
separated by 5cm in air and carrying currents of 40A in the same direction.
Hints:
Calculate the force per metre length using the formula
F/L = μI1I2 / 2ðd
In the same direction force is attractive.
10.Derive an expression for magnetic vector potential.
Hint:
magnetic vector potential is
A = μ / 4ð ///J / r dv
11.Derive the magnetic boundary relations.
i)The tangential component of the magnetic field is continuous across the boundary
.Ht1 = Ht2
ii)The normal component of the magnetic flux density is continuous across the boundary
Dn1 = Dn2
12.Find the magnetic field intensity at a distance ‘h’m above an infinite straight wire
carrying a steady current I.
Hints:
The magnetic flux density is calculated starting from Biot savarts law.
The magnetic flux density at any point due to an infinite long conductor is given by
B = μI / 2ðd
13.Two conducting concentric spherical shells with radii a and b are at potentials V0
and 0 respectively. Determine the capacitance of the capacitor.
Hint:
Derive the capacitance between concentric spheres using the formula
C = Q /V
= 4ðå [ ab /(b-a) ]
14State and derive an expression for Poyntings theorem.
Hints:
The net power flowing out of a given volume v is equal to the time rate of decrease of the energy stored within the volume minus the conduction losses.
15.Find the forces /length between two long straight parallel conductors carrying a
current of 10A in the same direction. A distance of 0.2m separates the conductors.
Also find the force/length when the conductors carry currents in opposite directions.
Hints:
Calculate the force per metre length using the formula
F/L = μI1I2 / 2ðd
In opposite direction force is repulsive
16 Derive an expression for torque acting on a loop.
Hints
When a current loop is placed parallel to a magnetic field forces act on the loop that
tends to rotate the tangential force times the radial distance at which it acts is
called torque or mechanicl moment of the loop.
T = m X B
17.Derive an expression for energy and energy density in a electric field.
Energy =CV2/2
Energy density = åE2/2
18. .Derive an expression for energy and energy density in a magnetic field.
Energy =LI2/2
Energy density = μH2/2
19.Derive all the maxwells equations.
Hints:
i)Maxwells equation from electric Gauss law.
ii) Maxwells equation from magnetic Gauss law.
iii)Maxwells equation from Amperes law.
iv) Maxwells equation from Faradays law.
20.Derive an expression for displacement, conduction current densities. Also obtain an
expression for continuity current relations
Hints:
Displacement current density Jd = åäE/ät
Conduction current density Jcond = óE
21.Derive the general Electromagnetic wave equation.
Hint:
Starting from the maxwells equation from Faradays law and Amperes law derive the
Equation
˘ 2 E - μ ó(ä E/ ät )-μå (ä2 E/ät2 )
22.Briefly explain reflection by a perfect dielectric when a wave is incident normally on a perfect dielectric and derive expression for reflection coefficient.
Hints:
When a plane electromagnetic wave is incident on the surface of a perfect dielectric part of the energy is transmitted and part of it is reflected.
Er / Ei = ( 2 – 1) /( 2 + 1)
23. Briefly explain reflection by a perfect dielectric when a wave is incident normally on a perfect conductor.
Hints
When the plane wave is incident normally upon the surface of a perfect conductor the
wave is entirely reflected. Since there can be no loss within a perfect conductor none of the energy is absorbed.
E (x,t) = 2Ei sinâx sinù t
24. Derive the relation between field theory and circuit theory for an RLC series circuit.
Hints :
Starting from field theory erquation for a series RLC circuit derive the circuit equation
V= IR + L dI/dt +(1 /C) / Idt
25.State and explain Faradays and Lenzs law of induction and derive maxwells equation.
Hints:
The total emf induced in a circuit is equal to the time rate of decrease of the total
magnetic flux linking the circuit.
˘ X E = -äB/ ät
The line integral of a vector around a closed path is equal to the surface integral of the normal component of its curl over any surface bounded by the path
H.dl = (ÑxH)ds
2.State coulombs law.
Coulombs law states that the force between any two point charges is directly
proportional to the product of their magnitudes and inversely proportional to the square
of the distance between them. It is directed along the line joining the two charges.
F=Q1Q2 / 4ðår2 ar
3.State Gauss law for electric fields
The total electric flux passing through any closed surface is equal to the total charge enclosed by that surface.
4.Define electric flux.
The lines of electric force is electric flux.
5.Define electric flux density.
Electric flux density is defined as electric flux per unit area.
6.Define electric field intensity.
Electric field intensity is defined as the electric force per unit positive charge.
E =F/ Q =Q/4ðår2 V/m
Electro Magnetic Theory
7.Name few applications of Gauss law in electrostatics.
Gauss law is applied to find the electric field intensity from a closed surface.e.g)Electric field can be determined for shell, two concentric shell or cylinders etc.
8.What is a point charge?
Point charge is one whose maximum dimension is very small in comparison with any
other length.
9.Define linear charge density.
It is the charge per unit length.
10.Write poisson’s and laplace ’s equations.
Poisson ‘s eqn:
Ñ2V= - ñv / å
Laplace’ s eqn:
Ñ2V= 0
11.State the condition for the vector F to be solenoidal.
Ñ·F =0
12. .State the condition for the vector F to be irrotational.
ÑxF =0
13.Define potential difference.
Potential difference is defined as the work done in moving a unit positive charge
from one point to another point in an electric field.
14.Define potential.
Potential at any point is defined as the work done in moving a unit positive charge
from infinity to that point in an electric field.
V=Q / 4ðår
15.Give the relation between electric field intensity and electric flux density.
D=åE C/m2
16.Give the relationship between potential gradiant and electric field.
E= - ÑV
17.What is the physical significance of div D ?
Ñ·D=-ñv
The divergence of a vector flux density is electric flux per unit volume leaving a small volume. This is equal to the volume charge density.
18. Define current density.
Current density is defined as the current per unit area.
J= I/A Amp/m2
19.Write the point form of continuity equation and explain its significance.
Ñ·J= - ñv / t
20.Write the expression for energy density in electrostatic field.
W=1 / 2 åE2
21.Write the boundary conditions at the interface between two perfect dielectrics.
i)The tangential component of electric field is continuous i.e)Et1=Et2
ii)The normal component of electric flux density is continuous I.e)Dn1=Dn2
22.Write down the expression for capacitance between two parallel plates.
C=åA / d
23.What is meant by displacement current?
Displacement current is nothing but the current flowing through capacitor.
J= D / t
24.State point form of ohms law.
Point form of ohms law states that the field strength within a conductor is
proportional to the current density.J=óE
25 Define surface charge density.
It is the charge per surface area.
26.State amperes circuital law.
Magnetic field intensity around a closed path is equal to the current enclosed by the
path. H·dl=I
27.State Biot –Savarts law.
It states that the magnetic flux density at any point due to current element is
proportional to the current element and sine of the angle between the elemental length
and inversely proportional to the square of the distance between them
dB=μ 0Idl sinè / 4ðr2
28.Define magnetic vector potential.
It is defined as that quantity whose curl gives the magnetic flux density.
B=Ñ x A =μ / 4ð J/r dv web/m2
29.Write down the expression for magnetic field at the centre of the circular coil.
H = I/2a.
30.Give the relation between magnetic flux density and magnetic field intensity.
B =μ H
31.Write down the magnetic boundary conditions.
i) The normal components of flux density B is continuous across the boundary.
ii) The tangential component of field intensity is continuous across the boundary.
32.Give the force on a current element.
dF = BIdlsinè
33..Define magnetic moment.
Magnetic moment is defined as the maximum torque per magnetic induction of
flux density. m=IA
34.State Gauss law for magnetic field.
The total magnetic flux passing through any closed surface is equal to zero.
B.ds =0
35.Define a wave.
If a physical phenomenon that occurs at one place at a given time is reproduced at
other places at later times , the time delay being proportional to the space separation
from the first location then the group of phenomena constitutes a wave.
36. Mention the properties of uniform plane wave.
i) At every point in space ,the electric field E and magnetic field H are perpendicular to each other.
ii)The fields vary harmonically with time and at the same frequency everywhere in
space.
37.Write down the wave equation for E and H in free space.
Ñ2H– μ 0å0
2H / t 2 =0.
38.Define intrinsic impedance or characteristic impedance.
It is the ratio of electric field to magnetic field.or It is the ratio of square root of permeability to permittivity of medium.
39.Give the characteristic impedance of free space.
377ohms
40.Define propagation constant.
Propagation constant is a complex number
ã =á +jâ
where á is attenuation constant
â is phase constant
ã = jùμ (ó +jùå)
41.Define skin depth
It is defined as that depth in which the wave has been attenuated to 1/e or
approximately 37% of its original value.
Ä = 1/á = 2 / jùó
42.Define Poynting vector.
The poynting vector is defined as rate of flow of energy of a wave as it propagates.
P =E X H
43. State Poyntings Theorem.
The net power flowing out of a given volume is equal to the time rate of decrease
of the the energy stored within the volume- conduction losses.
44.Give significant physical difference between poisons and laplaces equations.
When the region contains charges poisons equation is used and when
there is no charges laplaces equation is applied.
45.Give the difficulties in FDM.
FDM is difficult to apply for problems involving irregular boundaries and non
homogenious material properties.
46.Explain the steps in finite element method.
i) Discretisation of the solution region into elements.
ii) Generation of equations for fields at each element
iii) Assembly of all elements
iv) Solution of the resulting system
47.State Maxwells fourth equation.
The net magnetic flux emerging through any closed surface is zero.
48. State Maxwells Third equation
The total electric displacement through the surface enclosing a volume is equal to the total charge within the volume.
49.State the principle of superposition of fields.
The total electric field at a point is the algebraic sum of the individual electric field at that point.
50.Define ohms law at a point
Ohms law at appoint states that the field strength within a conductor is proportional
to current density.
51.Define self inductance.
Self inductance is defined as the rate of total magnetic flux linkage to the current
through the coil.
52.Define pointing vector.
The vector product of electric field intensity and magnetic field intensity at a point is a measure of the rate of energy flow per unit area at that point.
53.Give the formula to find potential at a point which is surrounded by four
orthogonal points in FDM.
V0= ¼(V1+V2+V3+V4)
54.Give the formula to find potential at a point which is surrounded by six
orthogonal points in FDM.
V0= ¼(V1+V2+V3+V4 +V5+V6)
55.State Lenz law.
Lenz’s law states that the induced emf in a circuit produces a current which opposes the change in magnetic flux producing it.
56.What is the effect of permittivity on the force between two charges?
Increase in permittivity of the medium tends to decrease the force between two
charges and decrease in permittivity of the medium tends to increase the force between
two charges.
57.State electric displacement.
The electric flux or electric displacement through a closed surface is equal to the charge enclosed by the surface.
58.What is displacement flux density?
The electric displacement per unit area is known as electric displacement density or
electric flux density.
59.What is the significance of displacement current?
The concept of displacement current was introduced to justify the production of
magnetic field in empty space. It signifies that a changing electric field induces a
magnetic field .In empty space the conduction current is zero and the magnetic fields are entirely due to displacement current.
60.Distinguish between conduction and displacement currents.
The current through a resistive element is termed as conduction current whereas the
current through a capacitive element is termed as displacement current.
61.Define magnetic field strength.
The magnetic field strength (H) is a vector having the same direction as magnetic flux
density.
H=B/μ
62.Give the formula to find the force between two parallel current carrying
conductors.
F=μI I1 / 2ðR
63.Give the expression for torque experienced by a current carrying loop situated in
a magnetic field.
T = IABsinè
64 What is torque on a solenoid?
T = NIABsinè
65.Explain the conservative property of electric field.
The work done in moving a point charge around a closed path in a electric field is zero. Such a field is said to be conservative.
E.dl = 0
66.Write he expression for field intensity due to a toroid carrying a filamentary
current ?
I H=NI / 2ïR
67.What are equipotential surfaces?
An equipotential surface is a surface in which the potential energy at every point is of the same vale.
68.Define loss tangent.
Loss tangent is the ratio of the magnitude of conduction current density to displacement current density of the medium.
Tan ä = ó / ùå
69.Defie reflection and transmission coefficients.
Reflection coefficient is defined as the ratio of the magnitude of the reflected field to that of the incident field.
70. Define transmission coefficients.
Transmission coefficient is defined as the ratio of the magnitude of the
transmitted field to that of incident field.
71.What will happen when the wave is incident obliquely over dielectric –dielectric
boundary?
When a plane wave is incident obliquely on the surface of a perfect dielectric part of the energy is transmitted and part of it is reflected .But in this case the transmitted wave will be refracted, that is the direction of propagation is altered.
72.What is the expression for energy stored in a magnetic field?
W = ½ LI2
73.What is energy density in magnetic field?
W = ½ μH2
74.Distinguish between solenoid and toroid.
Solenoid is a cylindrically shaped coil consisting of a large number of closely spaced turns of insulated wire wound usually on a non magnetic frame.
If a long slender solenoid is bent into the form of a ring and there by closed on itself it becomes a toroid.
75.Describe what are the sources of electric field and magnetic field?
Stationary charges produce electric field that are constant in time, hence the term
electrostatics. Moving charges produce magnetic fields hence the term magnetostatics.
76.What are the significant physical differences between Poisson ‘s and laplace ‘s
equations.
Poisson ‘s and laplace ‘s equations are useful for determining the electrostatic potential V in regions whose boundaries are known. When the region of interest contains charges poissons equation can be used to find the
potential.
When the region is free from charge laplace equation is used to find the potential.
77.State Divergence Theorem.
The integral of the divergence of a vector over a volume v is equal to the surface integral of the normal component of the vector over the surface bounded by the volume.
78.Give the expression for electric field intensity due to a single shell of charge
E = Q / 4ðår2
79.Give the expression for potential between two spherical shells
V= 1/ 4ð (Q1/a – Q2/b)
80.Define electric dipole.
Electric dipole is nothing but two equal and opposite point charges separated by a finite distance.
81.What is electrostatic force?
The force between any two particles due to existing charges is known as electrostatic
force, repulsive for like and attractive for unlike.
82.Define divergence.
The divergence of a vector F at any point is defined as the limit of its surface integral per unit volume as the volume enclosed by the surface around the point shrinks to zero.
83.How is electric energy stored in a capacitor?
In a capacitor, the work done in charging a capacitor is stored in the form of electric
energy.
84.What are dielectrics?
Dielectrics are materials that may not conduct electricity through it but on applying electric field induced charges are produced on its faces .The valence electron in atoms of a dielectric are tightly bound to their nucleus.
85.What is a capacitor?
A capacitor is an electrical device composed of two conductors which are separated
through a dielectric medium and which can store equal and opposite charges ,independent
of whether other conductors in the system are charged or not.
86.Define dielectric strength.
The dielectric strength of a dielectric is defined as the maximum value of electric field that can b applied to the dielectric without its electric breakdown.
87.What meaning would you give to the capacitance of a single conductor?
A single conductor also possess capacitance. It is a capacitor whose one plate is at
infinity.
88.Why water has much greater dielectric constant than mica.?
Water has a much greater dielectric constant than mica .because water ha a permanent
dipole moment, while mica does not have.
89.What is lorentz force?
Lorentz force is the force experienced by the test charge .It is maximum if the direction of movement of charge is perpendicular to the orientation of field lines.
90.Define magnetic moment.
Magnetic moment is defined as the maximum torque on the loop per unit magnetic
induction.
91.Define inductance.
The inductance of a conductor is defined as the ratio of the linking magnetic flux to the current producing the flux. L = NÔ / I
92.What is main cause of eddy current?
The main cause of eddy current is that it produces ohmic power loss and causes local
heating.
93.How can the eddy current losses be eliminated?
The eddy current losses can be eliminated by providing laminations. It can be proved
that the total eddy current power loss decreases as the number of laminations increases.
94.What is the fundamental difference between static electric and magnetic field
lines?
There is a fundamental difference between static electric and magnetic field lines .The tubes of electric flux originate and terminates on charges, whereas magnetic flux tubes are continuous.
95.What are uniform plane waves?
Electromagnetic waves which consist of electric and magnetic fields that are
perpendicular to each other and to the direction of propagation and are uniform in plane
perpendicular to the direction of propagation are known as uniform plane waves.
96.Write short notes on imperfect dielectrics.
A material is classified as an imperfect dielectrics for ó <<ùå, that is conduction current
density is small in magnitude compared to the displacement current density.
97.What is the significant feature of wave propagation in an imperfect dielectric ?
The only significant feature of wave propagation in an imperfect dielectric compared to
that in a perfect dielectric is the attenuation undergone by the wave.
98.What is the major drawback of finite difference method?
The major drawback of finite difference method is its inability to handle curved
boundaries accurately.
99.What is method of images?
The replacement of the actual problem with boundaries by an enlarged region or with
image charges but no boundaries is called the method of images.
100.When is method of images used?
Method of images is used in solving problems of one or more point charges in the
presence of boundary surfaces.
Part-B
1.Find the electric field intensity of a straight uniformly charged wire of length ‘L’m
and having a linear charge density of +ë C/m at any point at a distance of ‘h’ m.
Hence deduce the expression for infinitely long conductor.
Hints: Field due to charge element is given by:
dE = ëdi/ 4ðîr2
Ex=ë [cos á1+cosá2] /4ðåh
Ey=ë [sin á1-siná2] /4ðåh
For infinitely long conductor
E = ël / 4ðåh
2.Derive the boundary relations for electric fields.
Hints:
i)The tangential component of the electric field is continuous at the surface
.Et1 = Et2
ii)The normal component of the electric flux density is continuous if there is no surface
charge density.
Dn1 = Dn2
3.Find the electric field intensity produced by a point charge distribution at
P(1,1,1)caused by four identical 3nC point charges located at P1(1,1,0)
P2(-1,1,0) P3(-1,-1,0) and P4(1,-1,0).
Hints:
Find the field intensity at P by using the formula
Ep = 1/4åð[( Q1/r1p
2 u1p ) +(q2/r2p
2 u2p) +(q3/r3p
2 u3p)+(q4/r4p
2)u4p)]
4.A circular disc of radius ‘a’ m is charged with a charge density of óC/m2 .Find the
electric field intensity at a point ‘h’m from the disc along its axis.
Hints:
Find the field due to the tangential and normal components
Total field is given by
E =ñs /2å [1-cos á]
5. Four positive charges of 10–9 C each are situated in the XY plane at points
(0,0) (0,1) (1,0) and (1,1).Find the electric field intensity and potential at
(1/2 ,1/2).
Hints:
Find the field intensity at point using the formula
E = Q / 4ðår2 ur
Find the potential at point using the formula
V = Q / 4ðår
Find the field intensity at the point due to all four charges by using the superposition
principle.
6. Given a electric field E = (-6y/x2) x + 6/x y + 5 z .Find the potential difference VAB
given A(-7,2,1) and B( 4,1,2)
Hint:
Find the potential using the formula v=-/E.dl and substitute the points
7.Derive an expression for potential difference between two points in an electric
field.
Hint:
The potential difference between two points r1 and r2 is
V = V1 –V2
V = Q / 4ðår1 _ Q / 4ðår 2
8.Find the magnetic flux density at a point Z on the axis of a circular loop of radius ‘a’ that carries a direct current I.
Hints:
The magnetic flux density at a point due to the current element is given by
dB = μIdl / 4ð r2
B = μIa2 / 2(a2 + z2)3/2
9.Determine the force per meter length between two long parallel wires A and B
separated by 5cm in air and carrying currents of 40A in the same direction.
Hints:
Calculate the force per metre length using the formula
F/L = μI1I2 / 2ðd
In the same direction force is attractive.
10.Derive an expression for magnetic vector potential.
Hint:
magnetic vector potential is
A = μ / 4ð ///J / r dv
11.Derive the magnetic boundary relations.
i)The tangential component of the magnetic field is continuous across the boundary
.Ht1 = Ht2
ii)The normal component of the magnetic flux density is continuous across the boundary
Dn1 = Dn2
12.Find the magnetic field intensity at a distance ‘h’m above an infinite straight wire
carrying a steady current I.
Hints:
The magnetic flux density is calculated starting from Biot savarts law.
The magnetic flux density at any point due to an infinite long conductor is given by
B = μI / 2ðd
13.Two conducting concentric spherical shells with radii a and b are at potentials V0
and 0 respectively. Determine the capacitance of the capacitor.
Hint:
Derive the capacitance between concentric spheres using the formula
C = Q /V
= 4ðå [ ab /(b-a) ]
14State and derive an expression for Poyntings theorem.
Hints:
The net power flowing out of a given volume v is equal to the time rate of decrease of the energy stored within the volume minus the conduction losses.
15.Find the forces /length between two long straight parallel conductors carrying a
current of 10A in the same direction. A distance of 0.2m separates the conductors.
Also find the force/length when the conductors carry currents in opposite directions.
Hints:
Calculate the force per metre length using the formula
F/L = μI1I2 / 2ðd
In opposite direction force is repulsive
16 Derive an expression for torque acting on a loop.
Hints
When a current loop is placed parallel to a magnetic field forces act on the loop that
tends to rotate the tangential force times the radial distance at which it acts is
called torque or mechanicl moment of the loop.
T = m X B
17.Derive an expression for energy and energy density in a electric field.
Energy =CV2/2
Energy density = åE2/2
18. .Derive an expression for energy and energy density in a magnetic field.
Energy =LI2/2
Energy density = μH2/2
19.Derive all the maxwells equations.
Hints:
i)Maxwells equation from electric Gauss law.
ii) Maxwells equation from magnetic Gauss law.
iii)Maxwells equation from Amperes law.
iv) Maxwells equation from Faradays law.
20.Derive an expression for displacement, conduction current densities. Also obtain an
expression for continuity current relations
Hints:
Displacement current density Jd = åäE/ät
Conduction current density Jcond = óE
21.Derive the general Electromagnetic wave equation.
Hint:
Starting from the maxwells equation from Faradays law and Amperes law derive the
Equation
˘ 2 E - μ ó(ä E/ ät )-μå (ä2 E/ät2 )
22.Briefly explain reflection by a perfect dielectric when a wave is incident normally on a perfect dielectric and derive expression for reflection coefficient.
Hints:
When a plane electromagnetic wave is incident on the surface of a perfect dielectric part of the energy is transmitted and part of it is reflected.
Er / Ei = ( 2 – 1) /( 2 + 1)
23. Briefly explain reflection by a perfect dielectric when a wave is incident normally on a perfect conductor.
Hints
When the plane wave is incident normally upon the surface of a perfect conductor the
wave is entirely reflected. Since there can be no loss within a perfect conductor none of the energy is absorbed.
E (x,t) = 2Ei sinâx sinù t
24. Derive the relation between field theory and circuit theory for an RLC series circuit.
Hints :
Starting from field theory erquation for a series RLC circuit derive the circuit equation
V= IR + L dI/dt +(1 /C) / Idt
25.State and explain Faradays and Lenzs law of induction and derive maxwells equation.
Hints:
The total emf induced in a circuit is equal to the time rate of decrease of the total
magnetic flux linking the circuit.
˘ X E = -äB/ ät
Tuesday, June 8, 2010
Micro Processor Questions
Micro Processor Questions: " 
"
- What are the various registers in 8085? - Accumulator register, Temporary register, Instruction register, Stack Pointer, Program Counter are the various registers in 8085 .
- In 8085 name the 16 bit registers? - Stack pointer and Program counter all have 16 bits.
- What are the various flags used in 8085? - Sign flag, Zero flag, Auxillary flag, Parity flag, Carry flag.
- What is Stack Pointer? - Stack pointer is a special purpose 16-bit register in the Microprocessor, which holds the address of the top of the stack.
- What is Program counter? - Program counter holds the address of either the first byte of the next instruction to be fetched for execution or the address of the next byte of a multi byte instruction, which has not been completely fetched. In both the cases it gets incremented automatically one by one as the instruction bytes get fetched. Also Program register keeps the address of the next instruction.
- Which Stack is used in 8085? - LIFO (Last In First Out) stack is used in 8085.In this type of Stack the last stored information can be retrieved first.
- What happens when HLT instruction is executed in processor? - The Micro Processor enters into Halt-State and the buses are tri-stated.
- What is meant by a bus? - A bus is a group of conducting lines that carriers data, address, & control signals.
- What is Tri-state logic? - Three Logic Levels are used and they are High, Low, High impedance state. The high and low are normal logic levels & high impedance state is electrical open circuit conditions. Tri-state logic has a third line called enable line.
- Give an example of one address microprocessor? - 8085 is a one address microprocessor.
- In what way interrupts are classified in 8085? - In 8085 the interrupts are classified as Hardware and Software interrupts.
- What are Hardware interrupts? - TRAP, RST7.5, RST6.5, RST5.5, INTR.
- What are Software interrupts? - RST0, RST1, RST2, RST3, RST4, RST5, RST6, RST7.
- Which interrupt has the highest priority? - TRAP has the highest priority.
- Name 5 different addressing modes? - Immediate, Direct, Register, Register indirect, Implied addressing modes.
- How many interrupts are there in 8085? - There are 12 interrupts in 8085.
- What is clock frequency for 8085? - 3 MHz is the maximum clock frequency for 8085.
- What is the RST for the TRAP? - RST 4.5 is called as TRAP.
- In 8085 which is called as High order / Low order Register? - Flag is called as Low order register & Accumulator is called as High order Register.
- What are input & output devices? - Keyboards, Floppy disk are the examples of input devices. Printer, LED / LCD display, CRT Monitor are the examples of output devices.
- Can an RC circuit be used as clock source for 8085? - Yes, it can be used, if an accurate clock frequency is not required. Also, the component cost is low compared to LC or Crystal.
- Why crystal is a preferred clock source? - Because of high stability, large Q (Quality Factor) & the frequency that doesn’t drift with aging. Crystal is used as a clock source most of the times.
- Which interrupt is not level-sensitive in 8085? - RST 7.5 is a raising edge-triggering interrupt.
- What does Quality factor mean? - The Quality factor is also defined, as Q. So it is a number, which reflects the lossness of a circuit. Higher the Q, the lower are the losses.
- What are level-triggering interrupt? - RST 6.5 & RST 5.5 are level-triggering interrupts.
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