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. Magetic field energy in the inductor
C. Power delivered by the battery
D. Emf induced int the inductor

Answer

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

### Step-by-Step Solution:

1. **Understanding the Circuit**:
- An LR circuit contains an inductor and a resistor connected to a battery. When the switch is closed, the circuit is completed, and current can start to flow.

2. **Initial Conditions**:
- At \( t = 0 \), when the switch is first closed, the current in the circuit is initially zero. This is because inductors oppose changes in current due to their property of self-inductance.

3. **Current in the Circuit**:
- The current \( I \) in the circuit can be described by the equation:
\[ I(t) = \frac{V}{R} (1 - e^{-\frac{R}{L}t}) \]
- At \( t = 0 \), substituting \( t = 0 \) gives \( I(0) = 0 \).

4. **Magnetic Field Energy**:
- The magnetic field energy stored in the inductor is given by:
\[ U = \frac{1}{2} L I^2 \]
- Since \( I = 0 \) at \( t = 0 \), the magnetic field energy \( U \) is also zero.

5. **Power Delivered by the Battery**:
- The power \( P \) delivered by the battery can be calculated using the formula:
\[ P = V \cdot I \]
- At \( t = 0 \), since \( I = 0 \), the power \( P \) is also zero.

6. **Induced EMF**:
- The induced electromotive force (EMF) in the inductor can be expressed as:
\[ E = -L \frac{di}{dt} \]
- Although the current \( I \) is zero at \( t = 0 \), the rate of change of current \( \frac{di}{dt} \) is not zero because the current will start to increase from zero. Therefore, the induced EMF \( E \) is not zero.

### Conclusion:
The quantity that is **not zero** just after the connection is the **induced EMF** in the inductor.

### Final Answer:
The induced EMF is not zero just after the connection.

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