Copyright 20 13 Dorling Kindersley (India) Pvt. Ltd

4.4 
source trAnsformAtIon theorem And Its use In nodAl AnAlysIs
We take up the case where an independent voltage source is connected in series with a resistor. This 
case can indeed be solved by the procedure developed in the last section. However, there is a better 
way. We need the Source Transformation Theorem to understand this better method.
4.4.1 
source transformation theorem
It was pointed out in Chapter 1 that practical voltage sources can often be modelled as ideal independent 
voltage source in series with a resistance. Similarly, practical current sources can be modelled by 
an ideal independent current source in parallel with a resistance. Consider a pair of such practical 
sources delivering power to identical load resistors as shown in the circuits in Fig. 4.4-1(a) and (b).
v(t) is the voltage appearing across the load resistor and i(t) is the current through it in both cases.
R
Sv
R
L
v
S
(
t
)
v
(
t
)
i
(
t
)
(a)
+
+
–
–
R
L
R
Si
i
S
(
t
)
v
(
t
)
i
(
t
)
(b)
+
–
Fig. 4.4-1 
Practical voltage and current sources supplying power to identical load resistors
Applying Ohm’s law and KVL, we get 
v t
v t
R i t
s
sv
( )
( )
( )
=
−
in the circuit in Fig. 4.4-1(a) and 
applying current division principle and Ohm’s law we get
v t
R R
R
R
i t
R i t
R
R
R
R i t
R i
L
si
si
L
s
si s
si
si
L
si s
si
( )
( )
( )[
]
( )
(
=
+
=
−
+
=
−
1
tt
) in the circuit in Fig. 4.4-1 (b). What 
are the conditions such that the voltage developed across the load resistor is the same in both cases?
The required conditions are (i) 
R
R
R
sv
si
s
=
=
and (ii)
v t
R i t
s
s s
( )
( )
=
. The sources are indistinguishable 
from their terminal behaviour if these two conditions are satisfied. That is, if the source is put inside 

---

4.16
Nodal Analysis and Mesh Analysis of Memoryless Circuits
a black box and an effort is made to determine whether it is a voltage source or a current source by 
measuring v(t) and/or i(t) for various values of R
L
, such an attempt will fail. The two sources in Fig. 
4.4-1 are completely equivalent as far as their effect on external element is concerned and one may 
replace the other provided they satisfy the two conditions listed above. Note that the equivalence is 
only with respect to what happens to the external element. They are not equivalent as far as what 
happens inside the source is concerned. For instance, the power dissipation in R
S
 is not the same in the 
two sources for the same value of R
L
.
Source Transformation Theorem states that a voltage source with source function 
v
S
(
t
) 
in series with a resistance 
R
S
can be replaced by a current source with source function 
i
S
(
t
) 
=
v
S
(
t
) /
R
S
in parallel with a resistance 
R
S
without affecting any voltage/current/
power variable external to the source. The direction of current source is such that 
current flows out of the terminal at which the positive of the voltage source is presently 
connected. 
Similarly, a current source with source function 
i
S
(
t
) in parallel with a resistance 
R
S
can be replaced by a voltage source with source function 
v
S
(
t
) 
=
R
S
i
S
(
t
) in series with 
a resistance 
R
S
without affecting any voltage/current/power variable external to the 
source. The polarity of voltage source is such that it tends to establish a current in 
the external circuit in the same direction as in the case when the current source is 
acting. 
The reasoning employed in arriving at this theorem is equally valid in the case of dependent 
sources too. Hence, Source Transformation Theorem is applicable to dependent sources 
also.
Fig. 4.4-2 states the Source Transformation Theorem 
graphically.