The coefficient of self-induction of two coils are 0.01 H and 0.03 H respectively. If they oppose each other then the resultant self induction will be, if M = 0.01 H

Options

A. 2H
B. `0.2 H`
C. `0.02H`
D. zero

Answer

To solve the problem, we need to calculate the resultant self-inductance of two coils that oppose each other. The coefficients of self-inductance for the two coils are given as follows:

- \( L_1 = 0.01 \, \text{H} \)
- \( L_2 = 0.03 \, \text{H} \)
- Mutual inductance \( M = 0.01 \, \text{H} \)

When two coils oppose each other, the formula for the resultant self-inductance \( L_R \) is given by:

\[ L_R = L_1 + L_2 - 2M \]

### Step-by-Step Solution:

1. **Identify the values**:
- \( L_1 = 0.01 \, \text{H} \)
- \( L_2 = 0.03 \, \text{H} \)
- \( M = 0.01 \, \text{H} \)

2. **Substitute the values into the formula**:
\[ L_R = 0.01 + 0.03 - 2 \times 0.01 \]

3. **Calculate the sum of \( L_1 \) and \( L_2 \)**:
\[ L_1 + L_2 = 0.01 + 0.03 = 0.04 \, \text{H} \]

4. **Calculate \( 2M \)**:
\[ 2M = 2 \times 0.01 = 0.02 \, \text{H} \]

5. **Subtract \( 2M \) from the sum**:
\[ L_R = 0.04 - 0.02 = 0.02 \, \text{H} \]

6. **Final Result**:
The resultant self-inductance \( L_R \) is:
\[ L_R = 0.02 \, \text{H} \]

### Conclusion:
The resultant self-inductance of the two coils when they oppose each other is \( 0.02 \, \text{H} \).