Question

A galvanometer of 500Ω resistance is shunted such that only 4% of the current passes through the galvanometer. Find the shunt resistance.

• A. 12.5Ω
• B. 15Ω
• C. 18Ω
• D. 20Ω

Hint:

For shunt resistance calculations, use the formula \( R_s = \frac{R}{\frac{I_s}{I} - 1} \), where \( R \) is the resistance of the galvanometer and \( \frac{I_s}{I} \) is the fraction of current passing through it.

Answer 1

The Correct Option is A

Step 1: Use the formula for shunt resistance.
The shunt resistance \( R_s \) can be calculated using the formula: \[ R_s = \frac{R}{\frac{I_s}{I} - 1} \] Where:
- \( R \) is the resistance of the galvanometer (500Ω),
- \( I_s/I \) is the fraction of the total current passing through the galvanometer (4% or 0.04).

Step 2: Substituting the given values.
Substitute \( R = 500Ω \) and \( \frac{I_s}{I} = 0.04 \): \[ R_s = \frac{500}{\frac{0.04}{1} - 1} = \frac{500}{0.04 - 1} = \frac{500}{-0.96} = 12.5Ω \]
Final Answer: 12.5Ω.