A galvanometer of resistance G can be converted into a voltmeter of range `theta-V` volts by connecting a resistance R in series with it. How much resistance will be required to change its range from 0 to `V//2`?

Explanation

To solve the problem, we need to determine the resistance \( R' \) required to change the range of the galvanometer from \( 0 \) to \( \frac{V}{2} \) volts. We will start by using the relationship between the galvanometer's resistance, the series resistance, and the voltage range.

### Step-by-Step Solution:

1. **Understanding the Initial Setup**:
- Let the resistance of the galvanometer be \( G \).
- When connected in series with a resistance \( R \), the galvanometer can measure a voltage \( V \).
- The current through the galvanometer when measuring \( V \) is given by:
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