A galvanometer of resistance `100Omega` gives full scale deflection for `10mA` current. What should be the value of shunt, so that it can measure a current of 100mA?

Answer

To solve the problem of finding the value of the shunt resistor needed for a galvanometer to measure a current of 100 mA, we can follow these steps:

### Step-by-Step Solution

1. **Understand the Given Information:**
- Resistance of the galvanometer, \( R_g = 100 \, \Omega \)
- Full scale deflection current of the galvanometer, \( I_g = 10 \, \text{mA} = 10 \times 10^{-3} \, \text{A} \)
- Total current to be measured, \( I = 100 \, \text{mA} = 100 \times 10^{-3} \, \text{A} \)

2. **Use the Formula for Shunt Resistor:**
The formula for the shunt resistor \( R_s \) is given by:
\[ R_s = \frac{R_g \cdot I_g}{I - I_g} \]

3. **Substitute the Values:**
- Substitute \( R_g = 100 \, \Omega \), \( I_g = 10 \times 10^{-3} \, \text{A} \), and \( I = 100 \times 10^{-3} \, \text{A} \) into the formula:
\[ R_s = \frac{100 \cdot (10 \times 10^{-3})}{(100 \times 10^{-3}) - (10 \times 10^{-3})} \]

4. **Calculate the Denominator:**
- Calculate \( I - I_g \):
\[ I - I_g = 100 \times 10^{-3} - 10 \times 10^{-3} = 90 \times 10^{-3} \, \text{A} \]

5. **Complete the Calculation:**
- Now substitute back into the equation:
\[ R_s = \frac{100 \cdot (10 \times 10^{-3})}{90 \times 10^{-3}} = \frac{1000 \times 10^{-3}}{90 \times 10^{-3}} = \frac{1000}{90} \approx 11.11 \, \Omega \]

6. **Final Answer:**
- The value of the shunt resistor needed is approximately \( R_s \approx 11.11 \, \Omega \).