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?

Options

A. `11.11 Omega`
B. `1.1 Omega`
C. `9.9 Omega`
D. `4.4 Omega`

Answer

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

### Step-by-Step Solution:

1. **Identify Given Values:**
- Resistance of the galvanometer (G) = 100 Ω
- Full-scale deflection current of the galvanometer (Ig) = 10 mA = 10 × 10^(-3) A
- Total current to be measured (I) = 100 mA = 100 × 10^(-3) A

2. **Understand the Circuit Configuration:**
- The galvanometer is connected in parallel with the shunt resistor (Rs).
- The current through the galvanometer is Ig, and the current through the shunt resistor is (I - Ig).

3. **Apply the Voltage Equality in Parallel:**
- The voltage across the galvanometer (Vg) is equal to the voltage across the shunt resistor (Vs).
- Therefore, we can write the equation:
\[ Ig \cdot G = (I - Ig) \cdot Rs \]

4. **Rearranging the Equation:**
- From the above equation, we can express Rs as:
\[ Rs = \frac{Ig \cdot G}{I - Ig} \]

5. **Substituting the Values:**
- Substitute Ig = 10 × 10^(-3) A, G = 100 Ω, and I = 100 × 10^(-3) A into the equation:
\[ Rs = \frac{(10 \times 10^{-3}) \cdot 100}{(100 \times 10^{-3}) - (10 \times 10^{-3})} \]

6. **Calculating the Denominator:**
- Calculate I - Ig:
\[ I - Ig = 100 \times 10^{-3} - 10 \times 10^{-3} = 90 \times 10^{-3} A \]

7. **Final Calculation:**
- Substitute back into the equation for Rs:
\[ Rs = \frac{(10 \times 10^{-3}) \cdot 100}{90 \times 10^{-3}} = \frac{1000 \times 10^{-3}}{90 \times 10^{-3}} = \frac{1000}{90} = 11.11 \, \Omega \]

8. **Conclusion:**
- The value of the shunt resistor (Rs) required is approximately **11.11 Ω**.