Electrical circuits lecture notes b. Tech

Steps to Apply Super position Principle: 
1. Replace all independent sources with their internal resistances except one source. Find the 
output (voltage or current) due to that active source using nodal or mesh analysis.
 
2. Repeat step 1 for each of the other independent sources.
 
3. Find the total contribution by adding algebraically all the contributions due to the
independent sources. 
Example:
By Using the superposition theorem find I in the circuit shown in figure?
Fig.(a) 
Solution:
Applying the superposition theorem, the current 
I
2
in the resistance of 3 Ω due to the 
voltage source of 20V alone, with current source of 5A open circuited [ as shown in the figure.1 
below ] is given by : 
Fig1
 
I
2
= 20/(5+3) = 2.5A 
Similarly the current I
5
in the resistance of 3 Ω due to the current source of 5A alone with 
voltage source of 20V short circuited [ as shown in the figure.2 below ] is given by : 
Fig.2 

---

I
5
= 5 x 5/(3+5) = 3.125 A 
The total current passing through the resistance of 3Ω is then 
=
I
2
+ I
5
= 2.5 + 3.125 =
 
5.625 A 
Let us verify the solution using the basic nodal analysis referring to the node marked with V in 
fig.(a).Then we get : 
𝑉 − 20
5
+
𝑉
3
= 5
3V-60+5V=15
× 5
8V-60=75 
8V=135 
V=16.875 
The current I passing through the resistance of 
3Ω =
V/3 = 16.875/3 = 
5.625 A . 
Reciprocity theorem: 
Under Basic Electrical Engineering In many electrical networks it is found that if 
the positions of voltage source and ammeter are interchanged, the reading of ammeter remains 
the same. Suppose a voltage source is connected to a passive network and an ammeter is 
connected to other part of the network to indicate the response. Now any one interchanges the 
positions of ammeter and voltage source that means he or she connects the voltage source at the 
part of the network where the ammeter was connected and connects ammeter to that part of the 
network where the voltage source was connected. The response of the ammeter means current 
through the ammeter would be the same in both the cases. This is where the property of 
reciprocity comes in the circuit. The particular circuit that has this reciprocal property, is called 
reciprocal circuit.