Question

When a galvanometer is shunted by a resistance S, its current capacity increases n times. If the same galvanometer is shunted by another resistance S', its current capacity will increase to n' . The value of n' in terms of n, S, and S' is

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

Hint:

Express galvanometer resistance using the first shunt, then find the new multiplying factor for the second shunt.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
A shunt \(S\) across a galvanometer of resistance \(G\) increases its range \(n\) times when \(S=\dfrac{G}{n-1}\).

Step 2: Galvanometer resistance
From the first shunt, \(G=S(n-1)\).

Step 3: Second shunt
\(S'=\dfrac{G}{n'-1}\Rightarrow n'=1+\dfrac{G}{S'}\)

Step 4: Substitute
\(n'=1+\dfrac{S(n-1)}{S'}=\dfrac{S(n-1)+S'}{S'}\)

Final Answer:
The new range factor is \(\dfrac{S(n-1)+S'}{S'}\). \[ \boxed{\text{(C) }\dfrac{S(n-1)+S'}{S'}} \]