Question

In the network shown in Fig. , using Millman’s theorem, or otherwise find the voltage between A and B.

Answer 1

The end points of the different admittances which are connected directly to the common point B have been marked as 1, 2 and 3 as shown in the Fig. 

Incidentally, 40 Ω resistance will not be taken into consideration because it is not directly connected to the common point B. Here V₀₁ = V_A1 = −50 V ; V₀₂ = V_A2 = 100 V ; V₀₃ = V_A3 = 0 V.

∴ V₁₀₀' = VAb = ((-50/50) + (100/20) + (0/10))/((1/50) + (1/20) + (1/10)) = 23.5V

Since the answer comes out to be positive, it means that point A is at a higher potential as compared to point B. 

The detailed reason for not taking any notice of 40 Ω resistance are given in