For changing the range of a galvanometer with G ohm resistance fromV volt nV, what will be the value of resistance connected in sereis to it:-

Explanation

To solve the problem of determining the resistance \( R_s \) that needs to be connected in series with a galvanometer of resistance \( G \) ohms to change its range from \( V \) volts to \( nV \) volts, we can follow these steps:

### Step 1: Understand the relationship between voltage, current, and resistance
Initially, the galvanometer shows a maximum deflection at a voltage \( V \) when a current \( I \) flows through it. The relationship can be expressed using Ohm's law:
\[ V = I \cdot G \]

### Step 2: Introduce the series resistance
When we connect an additional resistance \( R_s \) in series with the galvanometer, the total voltage across the circuit when the current \( I \) flows is now \( nV \). The total voltage can be expressed as:
\[ nV = I \cdot R_s + I \cdot G \]

### Step 3: Rearrange the equation
We can factor out \( I \) from the right-hand side:
\[ nV = I (R_s + G) \]

### Step 4: Solve for the series resistance \( R_s \)
To isolate \( R_s \), we can rearrange the equation:
\[ R_s + G = \frac{nV}{I} \]
\[ R_s = \frac{nV}{I} - G \]

### Step 5: Substitute \( I \) in terms of \( V \)
From the initial relationship \( V = I \cdot G \), we can express \( I \) as:
\[ I = \frac{V}{G} \]
Substituting this into the equation for \( R_s \):
\[ R_s = \frac{nV}{\frac{V}{G}} - G \]
\[ R_s = nG - G \]
\[ R_s = (n - 1)G \]

### Conclusion
Thus, the resistance \( R_s \) that should be connected in series with the galvanometer to change its range from \( V \) volts to \( nV \) volts is:
\[ R_s = (n - 1)G \]