Question

Determine the current in each branch of the network shown in figure:

Answer 1

Current flowing through various branches of the circuit is represented in the given figure.

I₁ = Current flowing through the outer circuit 

I₂ = Current flowing through branch AB
I₃ = Current flowing through branch AD
I₂ − I₄ = Current flowing through branch BC
I₃ + I₄ = Current flowing through branch CD
I₄ = Current flowing through branch BD

For the closed circuit ABDA, potential is zero i.e.,
10I₂ + 5I₄ − 5I₃ = 0
2I₂ + I₄ −I₃ = 0
I₃ = 2I₂ + I₄ … (1)

For the closed circuit BCDB, potential is zero i.e.,
5(I₂ − I₄) − 10(I₃ + I₄) − 5I₄

 = 0 5I₂ + 5I₄ − 10I₃ − 10I₄ − 5I₄ = 0
5I₂ − 10I₃ − 20I₄ = 0
I₂ = 2I₃ + 4I₄ … (2)