Question

In an ammeter, 20 % of main current is passing through the galvanometer. If the resistance of the galvanometer is G, then the shunt resistance in ohm is

• A. \(\frac{G}{4}\)
• B. \(\frac{G}{8}\)
• C. \(\frac{G}{9}\)
• D. \(\frac{G}{10}\)

Hint:

The shunt is in parallel with the galvanometer, so the voltage across both is equal.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
An ammeter is a galvanometer with a shunt \( S \) in parallel. The potential difference across the galvanometer and the shunt is the same.

Step 2: Current Division
If the main current is \( I \), the galvanometer current is \( I_g = 0.2\,I = \frac{I}{5} \).
The shunt current is \( I - I_g = \frac{4I}{5} \).

Step 3: Calculation
\( I_g G = (I - I_g) S \)
\( \frac{I}{5}\,G = \frac{4I}{5}\,S \Rightarrow S = \frac{G}{4} \).

Step 4: Compare the options
The shunt resistance \( \frac{G}{4} \) is option (A).

Final Answer:
The shunt resistance is G/4. \[ \boxed{\text{(A) }\dfrac{G}{4}} \]