An LR circuit with a battery is connected at t=0. Which of the following quantities is not zero just after the connection?

Options

A. Current in the circuit
B. magnetic field energy
C. Power delivered by the battery
D. Emf induced in the inductor

Answer

To solve the problem, we need to analyze the behavior of an LR circuit (which consists of an inductor (L) and a resistor (R)) immediately after a battery is connected at time \( t = 0 \).

### Step-by-Step Solution:

1. **Understanding the Circuit Behavior at \( t = 0 \)**:
- When the circuit is first connected to the battery at \( t = 0 \), the inductor initially opposes any change in current due to its property of self-inductance. At this moment, the current \( I \) through the circuit is zero.

2. **Current \( I \)**:
- Since the inductor behaves like an open circuit at \( t = 0 \), the current \( I \) is equal to \( 0 \).
- Therefore, the option stating that the current is not zero is incorrect.

3. **Magnetic Field Energy \( U \)**:
- The magnetic energy stored in the inductor is given by the formula:
\[ U = \frac{1}{2} L I^2 \]
- Since \( I = 0 \) at \( t = 0 \), the magnetic energy \( U \) is also \( 0 \).
- Thus, the option stating that the magnetic field energy is not zero is incorrect.

4. **Power Delivered \( P \)**:
- The power delivered to the circuit can be calculated using the formula:
\[ P = V \cdot I \]
- Since \( I = 0 \) at \( t = 0 \), the power \( P \) is also \( 0 \).
- Therefore, the option stating that the power delivered is not zero is incorrect.

5. **Induced EMF \( \mathcal{E} \)**:
- The induced EMF in the inductor can be calculated using the formula:
\[ \mathcal{E} = L \frac{dI}{dt} \]
- At \( t = 0 \), although the current \( I \) is zero, the rate of change of current \( \frac{dI}{dt} \) is not zero because the current will start to increase from zero. Hence, the induced EMF \( \mathcal{E} \) is not zero.
- Therefore, the option stating that the induced EMF is not zero is correct.

### Conclusion:
The quantity that is not zero just after the connection of the LR circuit to the battery at \( t = 0 \) is the **induced EMF**.