difference and a current in a branch can be replaced by an ideal voltage source or an ideal current
source respectively.
The limitation of this theorem is that it cannot
be used to solve a network
containing two or more sources that are not in series or parallel.
Example: Using substitution theorem, draw equivalent branches for the branch ‘a-b’ of the
network of Fig.(a)?
Fig.(a)
Solution:
As per voltage division rule voltage across 3Ω and 2Ω resistance are
𝑉
3Ω
=
10 × 3
2 + 3
= 6𝑉
𝑉
2Ω
=
10 × 2
2 + 3
= 4𝑉
Current through the circuit is, I
=
10
2+3
=
2A
If we replace the 3Ω resistance with a voltage source of 6 V as shown in fig (1), then
Fig.(1)
Then according to Ohm’s Law the voltage across 2Ω resistance and current through the circuit is,
𝑉
2Ω
= 10 − 6 = 4𝑉
𝐼 =
10 − 6
2
= 2𝐴
Alternately if we replace 3Ω resistance with a current source of 2A as shown in Fig(2),then
Fig.(2)
Voltage across 2Ω is V
2Ω
= 10 – (3× 2) = 4 V and
Voltage across 2A current source is V
2A
= 10 - 4 = 6 V.
The voltage across 2Ω resistance and current through the circuit is unaltered i.e.
all initial condition of the circuit is intact.
Compensation Theorem:
It is one of the important theorems in Network Analysis , which finds its
application mostly in calculating the sensitivity of electrical networks & bridges and solving
electrical networks. In many circuits, after the circuit is analyzed, it is realized that only a small
change need to be made to a component to get a desired result. In such a case we would normally
have to recalculate. The compensation theorem allows us to compensate properly for such
changes without sacrificing accuracy.
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