Calculate the induced emf in a coil of 10 H inductance in which the current changes from 8A to 3A in 0.2 s.

Answer

To calculate the induced electromotive force (emf) in a coil with a given inductance when the current changes, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Inductance (L) = 10 H (Henries)
- Initial current (I_initial) = 8 A
- Final current (I_final) = 3 A
- Time interval (Δt) = 0.2 s

2. **Calculate the Change in Current (ΔI):**
- ΔI = I_final - I_initial
- ΔI = 3 A - 8 A = -5 A

3. **Use the Formula for Induced EMF:**
The formula for induced emf (ε) in terms of inductance and the rate of change of current is given by:
\[ ε = -L \frac{ΔI}{Δt} \]

4. **Substitute the Values into the Formula:**
- Substitute L = 10 H, ΔI = -5 A, and Δt = 0.2 s into the formula:
\[ ε = -10 \, \text{H} \times \frac{-5 \, \text{A}}{0.2 \, \text{s}} \]

5. **Calculate the Induced EMF:**
- First, calculate the fraction:
\[ \frac{-5 \, \text{A}}{0.2 \, \text{s}} = -25 \, \text{A/s} \]
- Now, substitute this back into the equation:
\[ ε = -10 \times (-25) = 250 \, \text{V} \]

6. **Final Result:**
- The induced emf in the coil is **250 V**.