Question

If a galvanometer is shunted by \((\frac{1}{n-1})^{th}\) of the value of its resistance, then the fraction of the total current passing through the galvanometer is

• A. \(\frac{1}{(n-1)}\)
• B. \(\frac{1}{n}\)
• C. \(\frac{n}{(n-1)}\)
• D. \(\frac{1}{1-n}\)

Hint:

Currents split in the ratio 1 : (n - 1).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
A shunt \(S\) is connected in parallel with the galvanometer \(G\). The current divides in inverse proportion to the resistances.

Step 2: Shunt value:
\(S=\dfrac G{n-1}\).

Step 3: Current through galvanometer:
\[ I_g=I\cdot\frac{S}{S+G}=I\cdot\frac{\frac G{n-1}}{\frac G{n-1}+G}=I\cdot\frac{1}{1+(n-1)}=\frac In \]

Step 4: Choose:
The fraction is \(\dfrac1n\), option (B).

Final Answer:
The fraction of current through the galvanometer is 1/n. \[ \boxed{\frac1n} \]