Question

Consider a galvanometer shunted with \( 5 \Omega \) resistance and \( 2% \) of current passes through it. What is the resistance of the given galvanometer ?

• A. \( 300 \Omega \)
• B. \( 245 \Omega \)
• C. \( 344 \Omega \)
• D. \( 226 \Omega \)

Hint:

If \( \frac{1}{n} \) of the total current passes through the galvanometer, then the galvanometer resistance is \( G = (n - 1)S \).
Here, \( I_g = \frac{2}{100} I = \frac{1}{50} I \), so \( n = 50 \).
\( G = (50 - 1) \times 5 = 49 \times 5 = 245 \Omega \).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
A shunt resistance \( S \) is connected in parallel with a galvanometer \( G \).
In a parallel combination, the potential difference across both components is the same.
Step 2: Key Formula or Approach:
Let \( I \) be the total current entering the system.
Current through galvanometer \( I_g \).
Current through shunt \( I_s = I - I_g \).
Equality of potential: \( I_g \times G = (I - I_g) \times S \).
Step 3: Detailed Explanation:
Given:
- \( S = 5 \Omega \).
- \( I_g = 2% \text{ of } I = 0.02I \).
- \( I - I_g = 100% - 2% = 98% \text{ of } I = 0.98I \).
Substitute into the formula:
\[ 0.02I \times G = 0.98I \times 5 \]
Divide both sides by \( I \):
\[ 0.02 \times G = 4.9 \]
\[ G = \frac{4.9}{0.02} = \frac{490}{2} \]
\[ G = 245 \Omega \]
Step 4: Final Answer:
The resistance of the galvanometer is \( 245 \Omega \).