A voltmeter has a resistance `G` and range `V`. Calculate the resistance to be used in series with it to extend its range to `nV`.

Options

A. `nG`
B. `(n - 1)G`
C. `G//m`
D. `G//(n - 1)`

Explanation

To solve the problem of calculating the resistance to be used in series with a voltmeter to extend its range from \( V \) to \( nV \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Components**:
- We have a voltmeter (which can be thought of as a galvanometer) with a resistance \( G \) and a range \( V \).
- We want to extend the range of this voltmeter to \( nV \).

2. **Current through the Voltmeter**:
- The current flowing through the voltmeter (galvanometer) when a voltage \( V \) is applied can be expressed using Ohm's Law:
\[ I_G = \frac{V}{G} \]
- Here, \( I_G \) is the current through the galvanometer.

3. **Total Voltage with Extended Range**:
- When we want to extend the range to \( nV \), the total voltage across the series combination of the voltmeter and the additional resistance \( S \) must equal \( nV \):
\[ nV = I_G \cdot (G + S) \]

4. **Substituting for \( I_G \)**:
- Substitute \( I_G \) from step 2 into the equation:
\[ nV = \left(\frac{V}{G}\right) \cdot (G + S) \]

5. **Simplifying the Equation**:
- Multiply both sides by \( G \) to eliminate the fraction:
\[ nVG = V(G + S) \]
- Now, divide both sides by \( V \) (assuming \( V \neq 0 \)):
\[ nG = G + S \]

6. **Solving for \( S \)**:
- Rearranging the equation gives:
\[ S = nG - G \]
- This simplifies to:
\[ S = G(n - 1) \]

7. **Conclusion**:
- The resistance \( S \) that needs to be added in series with the voltmeter to extend its range to \( nV \) is:
\[ S = G(n - 1) \]

### Final Answer:
The resistance to be used in series with the voltmeter to extend its range to \( nV \) is \( S = G(n - 1) \).

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