A coil has an inductance of `1.5 xx 10^(-2) H`. Calculate the emf induced, when current in the coil changes at the rate 200 A/s.

Answer

To solve the problem, we will use the formula for the induced electromotive force (emf) in a coil, which is given by:

\[ \text{EMF} (E) = L \frac{dI}{dt} \]

where:
- \( E \) is the induced emf in volts (V),
- \( L \) is the inductance in henries (H),
- \( \frac{dI}{dt} \) is the rate of change of current in amperes per second (A/s).

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Inductance \( L = 1.5 \times 10^{-2} \, \text{H} \)
- Rate of change of current \( \frac{dI}{dt} = 200 \, \text{A/s} \)

2. **Substitute the Values into the Formula:**
\[ E = L \frac{dI}{dt} \]
Substituting the values we have:
\[ E = (1.5 \times 10^{-2}) \times (200) \]

3. **Perform the Calculation:**
- First, calculate \( 1.5 \times 200 \):
\[ 1.5 \times 200 = 300 \]
- Now, multiply by \( 10^{-2} \):
\[ E = 300 \times 10^{-2} = 3 \, \text{V} \]

4. **Conclusion:**
The induced emf in the coil is:
\[ E = 3 \, \text{V} \]

### Final Answer:
The emf induced when the current in the coil changes at the rate of 200 A/s is **3 V**.

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