An inductor is connected to a battery through a switch. The emf induced in the inductor is much larger when the switch is opened as compared to the emf induced when the switch is closed. Is this statement true or false?

Explanation

To determine whether the statement "The emf induced in the inductor is much larger when the switch is opened as compared to the emf induced when the switch is closed" is true or false, we can analyze the behavior of inductors in both scenarios.

### Step-by-Step Solution:

1. **Understanding Induced EMF**:
The induced electromotive force (emf) in an inductor is given by Faraday's law of electromagnetic induction, which states that the induced emf (ε) is proportional to the rate of change of current (di/dt) through the inductor:
\[ \epsilon = -L \frac{di}{dt} \]
where \( L \) is the inductance of the inductor.

2. **Switch Closed**:
When the switch is closed, the current in the circuit gradually increases from zero to a steady-state value. The time taken for this increase is relatively long, as the inductor opposes changes in current. Therefore, the rate of change of current (di/dt) is small during this period.

3. **Switch Opened**:
When the switch is opened, the current in the circuit rapidly decreases to zero. The time taken for this decrease is very short. As a result, the rate of change of current (di/dt) is very large during this transition.

4. **Comparing Induced EMF**:
- When the switch is closed, the induced emf is small due to the slow change in current.
- When the switch is opened, the induced emf is large due to the rapid change in current.

5. **Conclusion**:
Since the induced emf is inversely proportional to the time taken for the change in current, and the time taken to decrease the current to zero (when the switch is opened) is much less than the time taken to increase the current to steady state (when the switch is closed), we conclude that:
\[ \text{Induced emf when switch is opened} > \text{Induced emf when switch is closed} \]
Therefore, the statement is **True**.