1
UNIT II
NETWORK REDUCTION AND NETWORK THEOREMS FOR DC AND AC
CIRCUITS
PART A
1) Define Lumped circuit
The circuit in which the elements are separated physically like resistors,
capacitors and inductors.
2) State division of current rule for a two branch parallel network
R1 and R2 are connected in parallel, Let I be the total current, I1 be the current
through R1, I2 be the current through R2 Then
I1 = I * R2/(R1+R2);
I2 = I * R1/(R1+R2)
I1 = (Other branch resistance / total resistance in the loop) * Total current
I2 = (Other branch resistance / total resistance in the loop) * Total current
3) State division of voltage rule for a circuit with three resistors in series.
R1 and R2 are connected in series, Let V be the total voltage, V1 be the voltage
across R1, V2 be the voltage across R2, Then,
V1 = V * R1/(R1+R2);
V2= V * R2(R1+R2)
V1 = (Branch Resistance / Total Resistance in the loop) * Source voltage
V2 = (Branch Resistance / Total Resistance in the loop) * Source voltage
4) What is the condition for source transformation?
Current sources in parallel can be added or subtracted depending on the
direction of current.
Voltage sources in series can be added or subtracted depending on their
polarities.
5) How to change the (a) current source into voltage source (b) voltage source
into current source?
(a) A current source I in parallel with a resistance R can be represented by a
voltage source V in series with a resistance R and magnitude of the voltage
source V = IR
EEE (2011-2012)
JEPPIAAR INSTITUTE OF TECHNOLOGY
EE2151 CIRCUIT THEORY
2
(b) Any voltage source V in series with a resistance R can be represented by an
equivalent circuit having a current source I in parallel with the resistance R
and the magnitude of the current source, I = V/R
6) Give one example problem of voltage to current source transformation?
7) With example explain the transformation of three voltage source is in
series with three resistance combination?
8) Write down the formulae for converting Star to Delta.
Rab=(RaRb+RbRc+RcRa) / Rc ;
Rbc=(RaRb+RbRc+RcRa) / Ra
Rca =(RaRb+RbRc+RcRa) / Rb
EEE (2011-2012)
JEPPIAAR INSTITUTE OF TECHNOLOGY
EE2151 CIRCUIT THEORY
3
9) Given that the resistors Ra, Rb and Rc are connected electrically in star. Write
the equations for resistors in equivalent delta.
10) Three equal resistors each of R ohms are connected in star. Find the value of
resistors in the equivalent delta.
11) Three resistors Rab, Rbc and Rca are connected in delta. Write the expression
for resistors in equivalent star.
12) Three resistors, each of value R ohms are connected in delta. Find the value of
resistors in its equivalent star.
13) Write the expression for converting delta connected resistances into an
equivalent star connected resistances.
EEE (2011-2012)
JEPPIAAR INSTITUTE OF TECHNOLOGY
EE2151 CIRCUIT THEORY
4
14) Each of the three arms of a delta connected network has resistance of 3ohm.
Find the equivalent star connected network.
15) A Y-connected resistive network consists of 2 ohm in each arm. Draw the
equivalent delta-connected network and insert the values
16) Give the expressions for star to delta transformation
17) Define Node and super node
A node is the point of connection of two or more branches.
A super node is formed by enclosing a voltage source connected between two
nodes.
18) Define mesh and super mesh.
A mesh is a loop, which does not contain any other loops within it.
A super mesh results when two meshes have a current source in common.
19) State Thevenin's theorem .
Thevenin’s theorem states that any circuit having a number of voltage sources,
resistances and open output terminals can be replaced by a simple equivalent
circuit consisting of a single voltage source in series with a
resistance(impedance), where the value of the voltage source is equal to the
resistance seen into the network across the output terminals.
EEE (2011-2012)
JEPPIAAR INSTITUTE OF TECHNOLOGY
EE2151 CIRCUIT THEORY
5
20) Draw the equivalent circuit for Thevenin’s theorem
21) What are the limitation of Thevenin’s Theorem?
The limitation of Thevenin’s theorem are,
1. Not applicable to the circuits consisting of nonlinear elements.
2. Not applicable to unilateral networks.
3. There should not be magnetic coupling between the load and circuit to be
replaced by Thevenin’s theorem
4. In the load side, there should not be controlled sources, controlled from some
other part of the circuit
22) Write the formula for finding the Thevenin’s resistance
Rth = (Vth / Isc)
Rth = Thevenins Resistance or Equivalent resistance
Vth = Thevenins Voltage or Open circuit Voltage
Isc = Short circuit current
23) State Norton's theorem.
Norton’s theorem states that any circuit with voltage sources, resistances
(impedances) and open output terminals can be replaced by a single current
source in parallel with single resistance (impedance), where the value of
current source is equal to the current passing through the short circuit output
terminals and the value of the resistance (impedance) is equal to the resistance
seen into the output terminals.
24) Draw the equivalent circuit for Norton’s theorem
EEE (2011-2012)
JEPPIAAR INSTITUTE OF TECHNOLOGY
EE2151 CIRCUIT THEORY
6
25) What is the formula for load current in Norton’s Theorem?
IL = (Isc * Rth) / (Rth + RL)
26) Compare Thevenin’s theorem and Norton’s theorem
Comparing Thevenin’s and Norton’s theorem, it is simple to justify that
IN = Vth / Rth . These two theorems are basically same, as the knowledge of one
equivalent circuit gives the other through a simple transformation of current
source in to voltage source.
27) Limitations of Thevenins and Nortons Theorem”
These theorems are not applicable to the circuits
1. Consisting of unilateral elements like diodes
2. Consisting of nonlinear elements like diode and transistor
3. Consisting of load series or parallel with controlled or dependent
sources
4. Consisting of magnetic coupling between load and any other circuit
elements.
28) State Superposition theorem.
The superposition theorem states that in any linear network containing two or
more sources, the response in any element is equal to algebraic sum of the
responses caused by individual sources acting alone, while the other sources
are non operative; that is, while considering the effect of individual sources,
other ideal voltage sources and ideal current sources in the network are
replaced by short circuit and open circuit across their terminals.
29) What is the limitation of super position theorem.
Super position theorem can be applied for finding the current through or
voltage across a particular element in a linear circuit containing more than two
sources. But this theorem cannot be used for the calculation of the power.
30) State Maximum power transfer theorem.
For a given Thevenin equivalent circuit, maximum power transfer occurs when
RL = RTH, that is, when the load resistance is equal to the thevenin resistance.
31) State the maximum power transfer theorem for AC circuit.
EEE (2011-2012)
JEPPIAAR INSTITUTE OF TECHNOLOGY
EE2151 CIRCUIT THEORY
7
Maximum average power is transferred to a load when the load impedance is
the complex conjugate of the Thevenin’s impedance as seen from the load
terminals, ZL = ZTh*
32) What is the current formula for Maximum power transfer theorem?
33) Where and why maximum power transfer theorem is applied.
In a certain applications it is desirable to have a maximum power transfer from
source to load. The maximum power transfer to load is possible only if the
source and load has matched impedance.
Eg: TV/Radio receiver
34) What is load matching?
Maximum power will be delivered from a source to a load when the load
impedance is equal to the source impedance. When this condition is satisfied
power delivered to the load is maximum and the load is said to be matched to
the source. This is called load matching.
35) The power delivered is maximum if the load impedance is equal to the
supply circuitimpedance – True or False.
36) What is the condition to obtain maximum power when an ac source with
internal impedance is connected to a load with variable resistance and
variable reactance.
Maximum power transferred from source to load, when the impedance is equal
to complex conjugate of source impedance.
37) Can the superposition theorem be applied to solve the electric circuits with
diodes present in the circuit? Why?
No, because diode is a nonlinear element.
38) A voltage source has internal impedance (4+j5) ohm. Find the load
impedance for maximum power transfer?
Load impedance = (4-j5) ohm for maximum power transfer.
39) What is the condition for maximum power transfer.
EEE (2011-2012)
JEPPIAAR INSTITUTE OF TECHNOLOGY
EE2151 CIRCUIT THEORY
8
40) Reciprocity Theorem:
In a linear bilateral active network a voltage source V volts in a branch gives
rise to a current I, If V is applied in the second branch, the current in the first
branch will be I. this V/I is called transfer impedance or resistance.
41) Sustitution Theorem:
Any portion of the network can be replaced by an equivalent branch, as long as
the potential and current in any other portion of the network remain unchanged.
42) Compensation Theorem:
It is the combination of substitution and superposition theorem
This theorem is used when it is desired to calculate the changes in the
magnitudes of currents and voltages when there is a small change in the
impedance of one of the branches.
43) Tellegens theorem:
In a linear or non linear, active or passive network the algebraic sum of all the
powers in all branches at any instant is zero or the power delivered by the
source is equal to the power dissipated in the circuit.
EEE (2011-2012)
JEPPIAAR INSTITUTE OF TECHNOLOGY
EE2151 CIRCUIT THEORY