UNIT- 4
NETWORK THEOREM-II
Q.1) Find the condition for maximum power transfer in the following network type DC
source, complex source impedance and complex load impedance but only load resistance
varying.
JAN.2015
Ans. : Let the network is replaced by Thevenin’s equivalent with an a.c. source and complex
source impedance. It is connected to a complex load with RL variable as shown in the Fig.
This is the required value of load resistance for maximum power transfer when load
impedance is complex with only load resistance varying
Q.2) Prove that an alternating voltage source transfers maximum power to a load when the
load impedance is the conjugate of the source impedance.
JUNE 2013
Sol : Let the given network is replaced by its Thevenin’s equivalent across the load terminals
as shown in the Fig.
Now for the load impedance ZL, both RL and XL are variable and are to be decided such that
power will be maximum. Hence according to maxima theorem we can write that for
maximum power transfer, with respect to variable XL and fixed RL,
Thus load reactance must be same in magnitude of the reactance of Zeq but opposite in sing.
Similarly power transfer will be maximum with respect to variable RL and fixed XL when,
Thus the resistance of load must be same that of equivalent impedance of the network. Thus,
when.ZL is the complex conjugate of Zeq, the power transfer to the load is maximum.
Q.3) A liner time invariant network when terminated with i) R = 1Ω, the current is 5‫ﮮ‬-450A
ii) XC = 1Ω, the current is 10‫ﮮ‬-450A. Find the Thevenin’s equivalent of the network. What
will be the current if it is terminated with XL = 1Ω?
JAN 2013
Q.4) Select values of R and C the network shown in fig. so that a maximum power is
delivered to R and calculate the value of that power V (t) = 250 sin 500t volts.
JUNE2014
(Q.5) Obtain the Thevenin’s equivalent of network shown in Fig. between terminals X and Y
JAN 2014
Q.6) In the circuit shown in fig find the load connected at AB for which the power transferred
will be maximum. Also find maximum power
JAN 2013
Ans. : for maximum power transfer. To find Zeq, replace voltage sources by short circuits.
To find the Pmax’ calculate VTH across A-B.
Q.7) “ Thevenin‟s equivalent is the dual of Norton‟s equivalent”. Comment on the above
statement and substantiate the same.
JAN 2013
Ans. : Consider a network shown in the Fig (a). The terminals A-B are the load terminals
where load impedance ZL is connected. According to the Norton’s theorem, the entire
network can be replaced by a current source IN and an equivalent impedance Zeq in parallel
with it, across the load terminals A-B as shown in the Fig. (b).
For obtaining the current IN , short the load terminals AB. Calculate the current through the
short circuited path by using any of the network simplification techniques. This is nothing but
Norton’s current IN. It is shown in the Fig.
This theorem is also called dual of the Thevenin‟s theorem. This is because, if the
Thevenin’s equivalent voltage source is converted to an equivalent current source, the
Norton’s equivalent is obtained. This is shown in the Fig.
Q.9) Obtain the Thevenin‟s and Norton‟s equivalent circuits across terminals A and B
for the circuit shown in Fig.
JUNE 2013
Sol. : 1) Thevenin‟s Theorem : Converting various voltage sources to current and current to
voltage we get,