The current in a coil is changed from 5A to 10A in `10^(-2)`s. Then, an emf of 50mV is induced in a coil near by it. Calculate mutual inductance of two coils.

Options

A. 100 `mu` H
B. 50 `mu` H
C. 20 `mu` H
D. 60 `mu` H

Answer

To solve the problem, we need to calculate the mutual inductance (M) of two coils based on the given information.

### Step-by-Step Solution:

1. **Identify the given values:**
- Initial current (I1) = 5 A
- Final current (I2) = 10 A
- Time interval (Δt) = \(10^{-2}\) s
- Induced emf (ε) = 50 mV = \(50 \times 10^{-3}\) V

2. **Calculate the change in current (ΔI):**
\[ \Delta I = I2 - I1 = 10 \, \text{A} - 5 \, \text{A} = 5 \, \text{A} \]

3. **Use the formula for induced emf:**
The formula relating induced emf (ε), mutual inductance (M), change in current (ΔI), and time interval (Δt) is:
\[ \epsilon = M \frac{\Delta I}{\Delta t} \]
Rearranging this formula to solve for mutual inductance (M):
\[ M = \frac{\epsilon \cdot \Delta t}{\Delta I} \]

4. **Substitute the known values into the formula:**
\[ M = \frac{(50 \times 10^{-3} \, \text{V}) \cdot (10^{-2} \, \text{s})}{5 \, \text{A}} \]

5. **Calculate the numerator:**
\[ 50 \times 10^{-3} \cdot 10^{-2} = 50 \times 10^{-5} = 5 \times 10^{-4} \, \text{V.s} \]

6. **Calculate mutual inductance (M):**
\[ M = \frac{5 \times 10^{-4}}{5} = 10^{-4} \, \text{H} \]

7. **Convert to microhenries:**
\[ M = 10^{-4} \, \text{H} = 100 \, \mu\text{H} \]

### Final Answer:
The mutual inductance of the two coils is **100 microhenries (100 µH)**.

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