A coil has a self inductance of 0.01H. The current through it is allowed to change at the rate of 1A in `10^(-2)s` . Calculate the emf induced.

Options

A. 1V
B. 2V
C. 1.5V
D. 2.5V

Answer

To solve the problem, we need to calculate the induced electromotive force (emf) in a coil with a given self-inductance when the current changes at a specific rate.

### Step-by-Step Solution:

1. **Identify the given values:**
- Self-inductance (L) = 0.01 H (Henry)
- Change in current (ΔI) = 1 A (Ampere)
- Change in time (Δt) = \(10^{-2}\) s (seconds)

2. **Use the formula for induced emf:**
The induced emf (E) in a coil due to a change in current is given by the formula:
\[ E = L \frac{ΔI}{Δt} \]
where:
- \(E\) is the induced emf,
- \(L\) is the self-inductance,
- \(ΔI\) is the change in current,
- \(Δt\) is the change in time.

3. **Substitute the values into the formula:**
\[ E = 0.01 \, \text{H} \times \frac{1 \, \text{A}}{10^{-2} \, \text{s}} \]

4. **Calculate the induced emf:**
- First, calculate the fraction:
\[ \frac{1 \, \text{A}}{10^{-2} \, \text{s}} = 100 \, \text{A/s} \]
- Now, substitute this back into the equation:
\[ E = 0.01 \, \text{H} \times 100 \, \text{A/s} = 1 \, \text{V} \]

5. **Final answer:**
The induced emf (E) is:
\[ E = 1 \, \text{V} \, \text{(Volt)} \]