Question

In the circuit shown the cells A and B have negligible resistances. For \( V_A = 12 \, \text{V} \), \( R_1 = 500 \, \Omega \) and \( R = 1000 \, \Omega \), the galvanometer \( G \) shows no deflection. The value of \( V_B \) is:

• A. 4 V
• B. 2 V
• C. 12 V
• D. 6 V

Hint:

For no deflection in a galvanometer, the potentials must balance across the resistances. Use Kirchhoff’s laws to solve for the potential differences in the circuit.

Answer 1

The Correct Option is B

Step 1: For the galvanometer to show no deflection, the current through it must be zero. This means the potential difference across the resistances must be balanced.
Step 2: Applying Kirchhoff's loop rule, we find that: \[ V_A - I R_1 = V_B \quad \text{where} \quad I = \dfrac{V_A - V_B}{R_1 + R}. \] Step 3: Solving for \( V_B \), we get \( V_B = 2 \, \text{V} \).
Final Answer: \[ \boxed{2 \, \text{V}} \]