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

Applying Kirchhoff’s laws to the circuit allows for the determination of branch currents. Initially, Kirchhoff’s current law is applied at point B, yielding:\[I_1 + I_2 = I_3\]Subsequently, Kirchhoff’s loop rule is applied to the closed loop AGFBA:\[3 + 2I_3 - 6 + 4I_2 + 2I_3 = 0\]This equation simplifies to:\[I_2 + I_3 = \frac{3}{4}\]This result is then substituted into another equation derived from the loop BFDCB:\[-4I_2 + 6 + 2I_1 - 6 + 2I_1 = 0\]This simplifies to:\[I_2 = I_1\]Solving these equations yields the following current values:\[I_1 = \frac{1}{4} \, \text{A}, \, I_2 = \frac{1}{4} \, \text{A}, \, I_3 = \frac{1}{2} \, \text{A}.\]