Question

In the given electrical network, the value of resistance ' $R$ ' when the current in the galvanometer will be zero, is

• A. $4\Omega$
• B. $6\Omega$
• C. $7\Omega$
• D. $10\Omega$

Hint:

Whenever a galvanometer current is zero in a bridge circuit, immediately think of the balanced bridge condition: \[ \frac{P}{Q}=\frac{R}{S} \] Then identify the four arms carefully from the diagram before solving.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
If galvanometer current is zero, the voltage at the node above it must match the battery voltage $6\text{ V}$.
Step 2: Key Formula or Approach:
Voltage divider rule: $V_R = V_{total} \times \frac{R}{R + R_{series}}$.
Step 3: Detailed Explanation:
$6 = 10 \times \frac{R}{R + 4} \implies 6R + 24 = 10R \implies 4R = 24 \implies R = 6\Omega$.
Step 4: Final Answer:
The value of $R$ is $6\Omega$.