1. UNIT – I
BASIC CIRCUITS ANALYSIS AND NETWORK TOPOLOGY
PART – A
1. State Ohms Law with its limitation. (May 2013)
At a constant temperature potential difference between two terminals is ditrectly
proportional to current flowing to the conductor
Limitations
Applicable only
i. for metallic conductor
ii. Only for linear devices
iii. Temperature should be constant
2. State Kirchhoff’s laws (Nov 2013, Nov 2015)
a. Kirchhoff`s Current Law
In a junction or node of a circuit the sum of current flowing towards to the junction
and sum of the current flowing away to the junction are equal
b. Kirchhoff`s Voltage Law
In a close loop sum of the potential drops and sum of the potential raise are equal
3. Define current
It is defined as the rate of change of flow of charge carriers in a conductor
I =
4. What is ideal source (May 2012)
A source, which delivers energy with specified voltage, which is independent of the
current supplied by the source and maintains constant voltage for all values of currents
supplied is called ideal source
5. Define potential
It is defined as the rate of change of work done with respect to charge of one coulomb
V or E =
6. Define graph of a network
A graph of any network can be drawn by placing all the nodes which are poins of
intersection of two or more branches.
7. Define a linear graph of a network
A linear graph is defined as a collection of various nodes and branches.
8. Define oriented graph
It is a graph in which the orientations of the branches are know in the given network and
the same are transferred on the graph. The oriented graph is also called directed graph.
9. Define planner graph
A planner graph drawn on a two-dimensional plane so the no two branches intersect at a
point which is not a node
10.Define sub-graph
A sub-graph is a subset of branches and nodes of a graph. There are two types of a sub-
graph. If the sub-graph contains branches and nodes less than the original graph such
graph is called sub-graph
11.Define tree
Tree is a set of branches with all nodes not forming any loop or closed path
2. 12.List the properties of tree
Tree contains all nodes on the graph
Tree does not contain any closed path
In a tree, there exists only one path between any pair of nodes
In a tree, minimum end nodes or terminal nodes are two
Every connected graph has at-lest one tree
The rank of the tree is same as that rank of graph (n-1)
Tree contain (n-1) branches if n are the nodes of the tree
13.Define cut-sets
A cut-set is a minimal set of branches of a connected graph such that after removal of
these branches graph gets separates into distinct parts, each of which a connected
graph, with the condition that replacing any one branch from the cut -sets makes the
graphs connected.
14.Define twig
A branch of a tree is called twig.
15.Define a co-tree
A set of branches forming a complement of a tree is called co-tree
16.Define chord or Link
The branches which are not in a tree are called chords or links
17.Define incidence matrix
An oriented graph can be completely explained or represented with the help of a matrix
known as incidence matrix
18.Write short notes on complete incidence matrix
The incidence matrix is nothing but a mathematical model to represent the given
network with all the information available. The information regarding the network is
nothing but which branches are incident at which node and what the orientations relative
to the nodes are. All the information are written in a matrix format called complete
incidence matrix ( )
19.State the properties of complete incidence matrix
The sum of the entries in any column is zero
The rank of the complete incidence matrix of a connected graph is n-1
The determinant of a loop of a complete incident matrix is always zero.
20.What is reduced incidence matrix
When any row from the complete incidence matrix is eliminated ny using mathamatical
manipulations, then the matrix is called reduced incidence matrix (A)
21.State the formula for number of possible trees in a graph.
Number of possible trees in a linear graph is = det {[A].[A]T }
Where
[A]- Reduced Incidence matrix
[A]T – Transpose of reduced incidence matrix
22.Define tie sets
The circuits formed by replacing each link in tree are called fundemental
circuits or f-circuits or tie-sets
23.What is cut-set
A connected graph can be separated into two parts by removing certain branches of the
graph. This is equivalent to cutting graph into two parts hence it is referred as cut-set.
24.Define link currents
In a closed path, there is a circulating current, which is also called the link current or
3. loop current
25.Define twig voltages
It is defined as branch voltages can be calculated by difference between the node
voltages.
26.State duality theorem
Two networks are said to be dual networks of each other if the mesh equations of given
network are the node equations of other network. T his network is based on Kirchhoff’s
current and voltage laws
27.List the dual elements
Element Dual element
Resistance Conductance
Capacitance Inductance
Series branch Parallel branch
Voltage source Current source
Closed switch Open switch
Charge Flux linkage
Mesh Node
Link Twig
Part – B
1. Find the current through each branch by network reduction technique.
2. Calculate a) the equivalent resistances across the terminals of the supply, b) total
current supplied by the source and c) power delivered to 16 ohm resistor in the circuit
shown in figure.
3. In the circuit shown, determine the current through the 2 ohm resistor and the total
current delivered by the battery. Use Kirchhoff’s laws.
4. 4. (i) Determine the current through 800 ohm resistor in the network shown in figure. (8)
(ii) Find the power dissipated in 10 ohm resistor for the circuit shown in figure. (8)
5. (i) In the network shown below, find the current delivered by the battery. (10)
(ii) Discuss about voltage and current division principles. (6)
6. (i) Explain :
Kirchoff laws. (4)
Dependent sources (2)
Source transformations (2) with relevant diagrams.
voltage division and current division rule (4)
(ii) Calculate the resistance between the terminals A – B. (4)
5. 7. i)Determine the value of V2 such that the current through the impedance (3+j4) ohm is
zero
ii) Find the current through branch a-b using mesh analysis shown in figure below.
8. Determine the mesh currents I1 and I2 for the given circuit shown below
9. Find the node voltages V1 and V2 and also the current supplied by the source for the
circuit shown below.
10. Find the nodal voltages in the circuit of figure.
11. i) Using the node voltage analysis, find all the node voltages and currents in 1/3 ohm
and 1/5 ohm resistances of figure.
6. ii) For the mesh-current analysis, explain the rules for constructing mesh impedance
matrix and solving the matrix equation [Z]I = V.
12. Solve for V1 and V2 using nodal method. Let V = 100V.
13. Using Mesh analysis, find current through 4 ohm resistor.
14. Use nodal voltage method to find the voltages of nodes ‘m’ and ‘n’ and currents
through j2 ohm and –j2 ohm reactance in the network shown below.
15. For the circuit shown find the current I flowing through 2 ohm resistance using loop
analysis.
7. UNIT – II
NETWORK THEOREMS FOR DC AND AC CIRCUITS
1. Write voltage division rule for the series circuit
; ;
2. Write current division rule for the voltage circuit
3. Convert the voltage source into current source
4. Convert the current source into voltage source
8. 5. Write the formula for star to delta conversion
6. Write the formula for delta to star conversion
9. 7. State Superposition theorem
In a linear network containing several sources the overall responses in any branch in
the network equals the algebraic sum of the responses of each individual source
separately with all other sources made inoperative (or) make short circuit.
(Note: voltage sources replaced by short circuit and current sources are replaced by
open circuit)
8. State the steps to solve the super position theorem.
Take only one independent voltage or current source
Obtain the branch currents
Repeat the above for
To determine the net ther sources branch current just adds the currents
obtained above.
9. What is the limitation of superposition theorem?
This theorem is valid only for linear systems. This theorem can be applied for
calculating the current through or voltage across in particular element. But this
superposition theorem is not applicable for calculation of the power.
10.State Thevenin’s theorem
Across a pair of terminals A.B any linear network can be replaced by an equivalent
circuit composed of a voltage source Vth in series with a resistance Rth and RL
Where
Vth - Thevenin voltage or opencircuit voltage measured in the open circuited terminal
AB
Rth – Thevenin resistance
RL – Load resistance
11.State the steps to solve the Thevenin’s theorem.
Remove the load resistance and find the open circuit voltage VO C
Deactivate the constant sources (fro voltage source remove it by internal
resistance & for current source delete the source by OC) and find the internal
resistance (RT H) of the source side looking through the open circuited load
terminals
Obtain the Thevenin’s equivalent circuit by connecting VOC in series with RT H
Reconnect the load resistance across the load terminals.
12.State Norton’s theorem
Any two terminal network containing linear, passive and active elements may be
replaced by an equivalent circuit with current source IN in parallel with a resistances
Rth or RN and RL
IN – current flowing through a short circuit placed across the terminals AB
10. Rth or RN – equivalent resistance of the N/W seen from the two terminals with all
indipandent sources replaced by internal resistance.
13.State the steps to solve the Norton’s theorem.
Remove the load resistor and find the internal resistance of the source N/W
by deactivating the constant source.
Short the load terminals and find the short circuit current
Norton’s equivalent circuit is drawn by keeping RTH in parallel with ISC
14.State maximum power transfer theorem
Maximum power is transferred from a source to the load when the load resistance is
made equal to the resistance of the network as viewed from the load terminals with
load removed and all the sources replaced by their internal resistance.
Note: - Determine the Thevenin`s equivalent circuit this will be the source
resistance.
15.Write some applications of maximum power transfer theorem.
Power amplifiers
Communication system
Microwave transmission
16.What is the Load current in a Norton’s circuit?
17.What is the load current in Thevenin’s circuit?
18.What is the maximum power in a circuit?
19.Write some applications of maximum power transfer theorem.
Power amplifiers
Communication system
Microwave transmission
20.What is the limitation of superposition theorem?
This theorem is valid only for linear systems. This theorem can be applied for
calculating the current through or voltage across in particular element. But this
superposition theorem is not applicable for calculation of the power.
11. 21.What are the limitations of maximum power transfer theorem?
The maximum efficiency can be obtained by using this theorem is only 50% . It is
because of 50% of the power is unnecessarily wasted in Rth. Therefore this theorem
only applicable for communication circuits and not for power circuits where efficiency
is greater importance rather than power delivered.
22.Define source transformation.
The current and voltage sources may be inter changed without affecting the
remainder of the circuit, this technique is the source transformation. It is the tool for
simplifying the circuit.
23.List the applications of Thevinins theorem.
It is applied to all linear circuits including electronic circuits represented by
the controlled source.
This theorem is useful when t is desired to know the effect of the response in
network or varying part of the network.
24.Explain the purpose of star delta transformation.
The transformation of a given set of resistances in star to delta or vice versa proves
extremely useful in circuit analysis and the apparent complexity of a given circuit can
sometime by very much reduce.
Part – B
1. (i) Find the value of R and the current flowing through it in the circuit shown when the
current in the branch OA is zero. (8)
ii) Determine the Thevenin’s equivalent for the figure (8)
2. Derive expressions for star connected arms in terms of delta connected arms and
delta connected arms in terms of star connected arms. (16)
3. Determine Thevenin’s equivalent across the terminals AB for the circuit shown in
figure below. (16)
12. 4. Find the Thevenins’s equivalent circuit of the circuit shown below, to left of the
terminals ab. Then find the current through RL = 16 ohm and 36 ohm. (16)
5. i) Find the current through branch a-b network using Thevenin’s theorem. (8)
ii) Find the current in each resistor using superposition principle of figure. (8)
6. i) Determine the Thevenin’s equivalent circuit. (8)
(ii) Determine the equivalent resistance across AB of the circuit shown in the figure
below. (8)
7. For the circuit shown, use superposition theorem to compute current I.
13. 8. (i)Compute the current in 23 ohm resistor using super position theorem for the circuit
shown below. (8)
(ii) Find the equivalent resistance between B and C in figure (8)
9. Using superposition theorem calculate current through (2+j3) ohm impedance branch
of the circuit shown.
10. i) For the circuit shown, determine the current in (2+j3) ohm by using superposition
theorem. (8)
ii) State and prove Norton’s theorem. (8)
11. i) Find the value of RL so that maximum power is delivered to the load resistance
shown in figure. 8)
14. ii) State and prove maximum power transfer theorem (8)
12. Determine the maximum power delivered to the load in the circuit. (16)
13. Find the value of impedance Z so that maximum power will be transferred from
source to load for the circuit shown. (16)
14. i) State and explain maximum power transfer theorem for variable Pure resistive
load. (8)
ii) Using Norton’s theorem, find current through 6 ohm resistance shown in figure.
UNIT – III RESONANCE AND COUPLED CIRCUITS
PART-A
1. What is meant by Resonance?
An A.C circuit is said to be resonance if it behaves as a purely resistive circuit. The
total current drawn by the circuit is then in phase with the applied voltage, and the
power factor will then unity. Thus at resonance the equivalent complex impedance of
the circuit has no j component.
2. Write the expression for the resonant frequency of a RLC series circuit.
Resonant frequency
3. What is resonant frequency?
The frequency at which resonance occurs is called resonant frequency.
15. At resonant frequency
4. Define series resonance.
A resonance occurs in RLC series circuit called series resonance. Under resonance
condition, the input current is in phase with applied voltage.
5. Define Quality factor.
The quality factor is defined as the ratio of maximum energy stored to the energy
dissipated in one period.
6. What are half power frequencies?
In RLC circuits the frequencies at which the power is half the max/min power are
called half power frequencies.
7. Write the characteristics of series resonance.
At resonance impedance in min and equal to resistance therefore current is max.
Before resonant frequency the circuit behaves as capacitive circuit and above
resonant frequency the circuit will behave as inductive circuit. At resonance the
magnitude of voltage across the inductance and capacitance will be Q times the
supply voltage but they are in phase opposition.
8. Define selectivity.
It is defined as the ratio of bandwidth and resonant frequency.
9. What is anti resonance?
In RLC parallel circuit the current is min at resonance whereas in series resonance
the current is max. Therefore the parallel resonance is called anti resonance.
10.Write the characteristics of parallel resonance.
At resonance admittance in min and equal to conductance therefore the current is
min. Below resonant frequency the circuits behave as inductive circuit and above
resonant frequency the circuit behaves as capacitive circuit. At resonance the
magnitude of current through inductance and capacitance will be q times the current
supplied by the source but they are in phase opposition.
11.What is Bandwidth and selectivity?
The frequency band within the limits of lower and upper half frequency is called
bandwidth.
Selectivity is the ratio of fr to the bandwidth
12.What are coupled circuits?
It refers to circuit involving elements with magnetic coupling. If the flux produced by
an element of a circuit links other elements of the same circuit then the elements are
said to be magnetic coupling.
13.What is meant by coupled circuits?
When two or more coils are linked by magnetic flux, then the coils are called coupled
circuits.
14.State the properties of a series RLC circuit.
The applied voltage and the resulting current are in phase, when also means than
the power factor of RLC circuit is unity. The net reactance is zero at resonance and
the impedance does not have the resistive part only.
The current in the circuit is maximum and is V/R amperes
16. At resonance the circuit has got minimum impedance and maximum curret
Frequency of resonance is given by
15.State the properties of a parallel RLC circuit.
Power Factor is unity
Current at resonance is (V/(L/RC)) and is in phase with the applied voltage. The
value of current at resonance is minimum.
Net impedance at resonance is max: & is equal to L/RC
The admittance is min: and the net susceptance is zero at resonance.
16.Define self inductance.
When permeability is constant the self inductance of a coil is defined as the ratio of
flux linkage and current.
17.Define mutual inductance.
When permeability is constant the mutual inductance between two coupled coils is
defined as the ratio of flux linkage in one coil due to common flux and current
through another coil.
18.Define coefficient of coupling.
In coupled coils the coefficient of coupling is defined as the raction of the total flux
produced by one coil linking another coil.
19.What is DOT convention?
The sign of mutual induced emf depends on the winding sense and the current
through the coil. The winding sense is decided by the manufacturer and to inform the
user about the winding sense a dot is placed at one end of each coil. When current
enter at dotted end in one coil then the mutual induced emf in the other coil is
positive at dot end.
20.State dot rule for coupled circuit.
It states that in coupled coils current entering at the dotted terminal of one coil
induce an emf in second coil which is +ve at dotted terminal of second coil. Current
entering at the un dotted terminal of one coil induce an emf in second coil which is
+ve at un dotted terminal of second coil.
21.Define coefficient of coupling.
The amount of coupling between to inductively coupled coils is expressed in terms of
the coefficient of coupling.
Part –B
1. Derive bandwidth for a series RLC circuit as a function of resonant frequency.(16)
2. i) For the circuit below, find the value of ω so that current and source emf are in
phase. Also find the current at this frequency. (8)
17. ii) Discuss the characteristics of parallel resonance of a circuit having G,L and C. (8)
3. (i) A Pure resistor, a pure capacitor and a pure inductor are connected in
parallelacrossa 50Hz supply, find the impedance of the circuit as seen by the
supply.Alsofind the resonant frequency. (8)
(ii) When connected to a 230V, 50Hz single phase supply, a coil takes 10kVA and
8kVAR. For this coil calculate resistance, inductance of coil and power consumed.(8)
4. (i) In an RLC series circuit if ω1 and ω2 are two frequencies at which the magnitude
of the current is the same and if ωr is the resonant frequency, prove that ω2 r =
ω1ω2.
(ii) A series RLC circuit has Q = 75 and a pass band (between half power
frequencies) of 160 Hz. Calculate the resonant requency and the upper and lower
frequencies of the pass band. (8)
5. (i) Explain and derive the relationships for bandwidth and half power frequencies of
RLC series circuit. (8)
(ii) Determine the quality facto of a coil R = 10 ohm, L = 0.1H and C = 10Μf (8)
6. A series RLC circuit has R=20 ohm, L=0.005H and C = 0.2 x 10-6 F. It is fed from a
100V variable frequency source. Find i) frequency at which current is maximum ii)
impedance at this frequency and iii) voltage across inductance at this frequency.
7. A series RLC circuit consists of R=100 ohm, L = 0.02 H and C = 0.02 microfarad.
Calculate frequency of resonance. A variable frequency sinusoidal voltage of constant
RMS value of 50V is applied to the circuit. Find the frequenc y at which voltage across
L and C is maximum. Also calculate voltage across L and C is maximum. Also
calculate voltages across L and C at frequency of resonance. Find maximum current
in the circuit. (16)
8. In the parallel RLC circuit, calculate resonant frequency, bandwidth, Q-factor and
power dissipated at half power frequencies. (16)
UNIT – IV
TRANSIENT ANALYSIS
Part-A
18. 1. What is transient state?
If a network contains energy storage elements, with change in excitation, the current
and voltage change from one state to other state the behavior of the voltage or
current when it is changed from one state to another state is called transient state.
2. What is transient time?
The time taken for the circuit to change from one steady state to another steady
state is called transient time.
3. What is transient response?
The storage elements deliver their energy to the resistances; hence the response
changes with time, get saturated after sometime, and are referred to the transient
response.
4. Define time constant of RLC circuit.
The time taken to reach 63.2% of final value in a RL circuit is called the time
constant of RL circuit.
5. Define time constant of RC circuit.
The time to taken to reach 36.8% of initial current in an RC circuit is called the time
constant of RC circuit.
Time constant= RC
6. What is meant by natural frequency?
If the damping is made zero then the response oscillates with natural frequency
without any opposition, such a frequency is called natural frequency of oscillations.
7. Define damping ratio.
It is the ratio of actual resistance in the circuit to the critical resistance.
8. Write down the condition, for the response of RLC series circuit to be under
damped for step input.
The condition for the response of RLC series circuit to be under damped step input is
9. Write down the few applications of RL, RC, RLC circuits.
Coupling circuits
Phase shift circuits
Filters
Resonant circuits
AC bridge circuits
Transformers
10.Write down the condition fo the response of RLC sereis circuit to be over
damped for step input.
The condition for the response of RLC series circuit to be over damped for step input
is,
11.Define transient response.
19. The transient response is defined as the response or output of a circuit from the
instant of switching to attainment of steady state.
12. What is natural response?
The response of a circuit due to stored energy alone without external source is called
natural response or source free response.
13.What is forced response?
The response of the circuit due to the external source is called forced response.
14.Define apparent power.
The apparent power is defined as the product of magnitude of voltage and
magnitude of current.
15.What is power factor and reactive power?
The power factor is defined as the cosine of the phase difference between voltage
and current.
Power factor= cosθ
The reactive power of the circuit is defined as the sine of the phase angle.
Reactive power= sin θ
PART – B
1. In the circuit of the figure shown below, find the expression for the transient current
and the initial rate of growth of the transient current (16)
2. 2. In the circuit shown in figure, switch S is in position 1 for a long time and brought
to position 2 at time t=0. Determine the circuit current. (16)
3. A resistance R and 2 microfarad capacitor are connected in series across a 200V
direct supply. Across the capacitor is a neon lamp that strikes at 120V. Calculate R to
make the lamp strike 5 sec after the switch has been closed. If R = 5Megohm, how
long will it take the lamp to strike?
4. A Series RLC circuits has R=50 ohm, L= 0.2H, and C = 50 microfarad. Constant
voltage of 100V is impressed upon the circuit at t=0. Find the expression for the
transient current assuming initially relaxed conditions.
5. A Series RLC circuits with R=300 ohm, L=1H and C=100x10-6 F has a constant
voltage of 50V applied to it at t= 0. Find the maximum value of current ( Assume
zero initial conditions)
6. A step voltage V(t) = 100 u(t) is applied to a series RLC circuit with L=10H, R=2ohm
and C= 5F. The initial current in the circuit is zero but there is an initial voltage of
50V on the capacitor in a direction which opposes the applied source. Find the
expression for the current in the circuit.
20. 7. For a source free RLC series circuit, the initial voltage across C is 10V and the initial
current through L is zero. If L = 20mH, C=0.5 microfarad and R=100 ohm. Evaluate
i(t).
8. For the circuit shown in figure, find the voltage across the resistor 0.5 ohm when the
switch, S is opened at t=0. Assume that there is no charge on the capacitor and no
current in the inductor before switching
9. In the circuit shown in figure, find the current i. Assume that initial charge across the
capacitor is zero.
10. In the circuit shown in figure, the switch is closed at time t=0. Obtain i(t). Assume
zero current through inductor L and zero charge across C before closing the switch.
11. Derive an expression for current response of RLC series circuit transient. (16)
12. Derive an expression for current response of RC, RL series circuit transient with step
signal (16)
13. Derive an expression for current response of RC, RL series circuit transient with
impulse signal (16)
14. Derive an expression for current response of RC, RL series circuit transient with
exponential signal (16)
15. Derive an expression for current response of RC, RL series circuit transient with AC
sinusoidal signal (16)
16. Derive an expression for current response of RLC series circuit transient with step
signal (16)
21. 17. Derive an expression for current response of RLC series circuit transient with impulse
signal (16)
18. Derive an expression for current response of RLC series circuit transient with
exponential signal (16)
19. Derive an expression for current response of RLC series circuit transient with AC
sinusoidal signal (16)
UNIT – V TWO PORT NETWORKS
1. Define port
A pair of terminals at which an electrical signal may enter or leave a network is
called
2. Define two port network
A network consisting two pairs of terminals is called two port networks
3. List the driving point functions of two port network
i. Voltage gain
ii. Current gain
iii. Input or output or transfer impedance
iv. Input or output or transfer admittance
4. List the parameters of two port network
i. Z – parameters
ii. Y – parameters
iii. ABCD parameters
iv. Hybrid or h – parameters
5. Write the z- parameter equations for two port network
6. Write the Y- parameter equations for two port network
7. Write the h- parameter equations for two port network
8. Write the ABCD - parameter equations for two port network
22. 9. Why z-parameters are called open circuit impedance parameters?
The z-parameters are obtained by open circuiting two ports one at a time to obtain
all 4 parameters. Also all the parameters are represented as a ratio of port voltage to
port current. Hence z-parameters are called open circuit impedance parameters
10.Why y-parameters called short circuit admittance parameters?
The h-parameters are obtained by short circuiting both ports one at a time to obtain
all the 4 parameters are represented as ratios of port current to port voltage. Hence
y-parameters are called as short circuit admittance parameters
11.Why h-parameters are called hybrid parameters?
From the above equations - inputimpedance, - reverse voltage gain, -
forward current gain, - is output admittance. So all the four parameters are of
different types and also with different units. Hence it is mixture of different types of
parameters with different units. Hence
12.What is the use of h-parameters?
h-parameters are used to
analyze the AC amplifier using BJT amplifier
analyze the small signal BJT amplifier
13. What is mean by a symmetrical network?
A network is said to be symmetrical if the impedance measured at the other port
with remaining port open circuited
14.What do u mean by a reciprocal network?
A network is said to be reciprocal if the ratio of voltage at one port to the current at
other port is same to the ratio if the positions of voltage and current are
interchanged
15.List the various types of interconnection of two port network
i. Cascade
ii. Series
iii. Parallel
iv. Series – Parallel
Part – B
1. Derive the driving point functions of z – parameter of a two port network
2. Derive the driving point functions of y – parameter of a two port network
3. Derive the driving point functions of h – parameter of a two port network
4. Derive the driving point functions of ABCD – parameter of a two port network
5. Derive the driving point functions of cascade connection of a two, two port network
6. Derive the driving point functions of series connection of a two, two port network
7. Derive the driving point functions of parallel connection of a two, two port network
8. Derive the driving point functions of series - parallel connection of a two, two port
network