An ammeter has resistance `R_(0)` and range l what resistance should be connected in parallel with it to increase its range by nl ?

Options

A. `R_(0)//(n-1)`
B. `R_(0)//(n+1)`
C. `R_(0)//n`
D. None of these

Answer

To solve the problem, we need to determine the resistance that should be connected in parallel with an ammeter to increase its range by a factor of \( n \).

### Step-by-Step Solution:

1. **Understand the Given Parameters**:
- The ammeter has an internal resistance \( R_0 \).
- The original range of the ammeter is \( I \).
- We want to increase the range to \( nI \).

2. **Concept of Shunt Resistance**:
- To increase the range of the ammeter, we need to connect a shunt resistance \( S \) in parallel with the ammeter. This allows a portion of the current to bypass the ammeter, effectively increasing its range.

3. **Current Distribution**:
- Let the total current flowing through the circuit be \( nI \).
- The current through the ammeter will be \( I \) (the original current it can measure).
- Therefore, the current through the shunt resistance \( S \) will be \( (nI - I) = (n - 1)I \).

4. **Voltage Drop Across the Ammeter**:
- The voltage drop across the ammeter can be expressed as:
\[ V = I \cdot R_0 \]

5. **Voltage Drop Across the Shunt Resistance**:
- The voltage drop across the shunt resistance can be expressed as:
\[ V = (n - 1)I \cdot S \]

6. **Setting the Voltage Drops Equal**:
- Since both components are in parallel, the voltage drops across them must be equal:
\[ I \cdot R_0 = (n - 1)I \cdot S \]

7. **Cancelling \( I \) from Both Sides**:
- Assuming \( I \neq 0 \), we can divide both sides by \( I \):
\[ R_0 = (n - 1)S \]

8. **Solving for Shunt Resistance \( S \)**:
- Rearranging the equation gives us:
\[ S = \frac{R_0}{n - 1} \]

9. **Conclusion**:
- The required shunt resistance \( S \) that should be connected in parallel with the ammeter to increase its range by \( nI \) is:
\[ S = \frac{R_0}{n - 1} \]

### Final Answer:
The resistance that should be connected in parallel with the ammeter is \( \frac{R_0}{n - 1} \).