Question

When a resistance of 100 $\Omega$ is connected in series with a galvanometer of resistance 'G', its range is 'V'. To double its range, a resistance of 1000 $\Omega$ is connected in series. The value of 'G' is ______.

• A. 400 $\Omega$
• B. 800 $\Omega$
• C. 1000 $\Omega$
• D. 1200 $\Omega$

Hint:

When an instrument's range is extended $n$ times ($V_{new} = n \cdot V_{old}$), the new required total series resistance must simply be $n$ times the old total series resistance! $G + R_2 = n(G + R_1)$.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
A galvanometer is converted into a voltmeter by adding a high resistance $R$ in series. The range $V = I_g(G + R)$.

Step 2: Formula Application:
Case 1: $V = I_g(G + 100)$. Case 2: $2V = I_g(G + 1000)$.

Step 3: Explanation:
Divide Case 2 by Case 1: $\frac{2V}{V} = \frac{I_g(G + 1000)}{I_g(G + 100)} \implies 2 = \frac{G + 1000}{G + 100}$. $2(G + 100) = G + 1000$ $2G + 200 = G + 1000 \implies G = 800$ Ω.

Step 4: Final Answer:
The value of $G$ is 800 Ω.