Question

A current of 2 A flows in the system of conductors as shown in the figure. The potential difference \(V_P - V_R\) will be :

• A. -2V
• B. -1V
• C. +1V
• D. +2V

Hint:

Use current division in parallel branches and then apply Ohm’s law for potential differences.

Answer 1

The Correct Option is B

Concept: Use Kirchhoff’s laws and symmetry of network.

Step 1: Identify branches.
Two paths from Q to S:
• Upper: \(2\Omega + 3\Omega = 5\Omega\)
• Lower: \(3\Omega + 7\Omega = 10\Omega\)

Step 2: Current division.
\[ I_{upper} : I_{lower} = 10 : 5 = 2:1 \] Total current = 2A: \[ I_{upper} = \frac{4}{3}A, \quad I_{lower} = \frac{2}{3}A \]

Step 3: Potential difference.
From Q → P: \[ V_P - V_Q = - I_{upper} \cdot 2 = -\frac{8}{3} \] From Q → R: \[ V_R - V_Q = - I_{lower} \cdot 3 = -2 \]

Step 4: Final result.
\[ V_P - V_R = \left(-\frac{8}{3}\right) - (-2) = -\frac{2}{3} = -1V \]