Question

The figure shows a circuit with three ideal batteries. Find the magnitude and direction of currents in the branches AG, BF and CD.

 

Hint:

Kirchhoff’s laws are helpful for analyzing circuits with multiple batteries and resistors to determine currents and voltages.

Answer 1

By applying Kirchhoff’s laws to the circuit, we can determine the currents in the different branches. First, we use Kirchhoff’s current law at point B: \[ I_1 + I_2 = I_3 \] Next, applying Kirchhoff’s loop rule for the closed loop AGFBA: \[ 3 + 2I_3 - 6 + 4I_2 + 2I_3 = 0 \] Simplifying: \[ I_2 + I_3 = \frac{3}{4} \] We substitute this in another equation based on another loop, BFDCB: \[ -4I_2 + 6 + 2I_1 - 6 + 2I_1 = 0 \] Which simplifies to: \[ I_2 = I_1 \] By solving the equations, we find: \[ I_1 = \frac{1}{4} \, \text{A}, \, I_2 = \frac{1}{4} \, \text{A}, \, I_3 = \frac{1}{2} \, \text{A}. \]