An ammeter gives full scale deflection when current of 1.0 A is passed in it. To convert it into 10 A range ammeter, the ratio of its resistance and the shunt resistance will be

Options

A. `1:9`
B. `1:10`
C. `1:11`
D. `9:1`

Answer

To solve the problem of converting an ammeter that gives full-scale deflection at 1.0 A into a 10 A range ammeter, we need to find the ratio of the resistance of the ammeter (R) to the shunt resistance (S).

### Step-by-Step Solution:

1. **Understand the Given Values:**
- The full-scale deflection current of the ammeter (I') = 1.0 A
- The desired maximum current range of the ammeter (I) = 10 A

2. **Use the Formula for Shunt Resistance:**
The formula to calculate the shunt resistance (S) is given by:
\[ S = \frac{I' \cdot R}{I - I'} \]
where:
- \(I'\) is the full-scale deflection current,
- \(I\) is the total current,
- \(R\) is the resistance of the ammeter.

3. **Substitute the Values into the Formula:**
Plugging in the known values:
\[ S = \frac{1 \cdot R}{10 - 1} = \frac{R}{9} \]

4. **Find the Ratio of Resistance of Ammeter to Shunt Resistance:**
We need to find the ratio \( \frac{R}{S} \):
\[ \frac{R}{S} = \frac{R}{\frac{R}{9}} = 9 \]

5. **Conclusion:**
The ratio of the resistance of the ammeter (R) to the shunt resistance (S) is:
\[ \frac{R}{S} = 9:1 \]

### Final Answer:
The ratio of the resistance of the ammeter to the shunt resistance is 9:1.