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 in the inductor
C. Power delivered by battery
D. emf induced in the inductor

Explanation

To solve the problem, we need to analyze the behavior of an LR circuit (inductor and resistor) connected to a battery at time \( t = 0 \). We will evaluate the quantities: current, magnetic field, power delivered by the battery, and EMF induced in the inductor.

### Step-by-Step Solution:

1. **Understanding the Circuit at \( t = 0 \)**:
- When the circuit is connected to the battery at \( t = 0 \), the inductor initially behaves like an open circuit. This means that no current can flow through the circuit at this instant.

2. **Current in the Circuit**:
- Since the inductor acts as an open circuit at \( t = 0 \), the current \( I \) in the circuit is:
\[ I = 0 \, \text{A} \]

3. **Magnetic Field in the Circuit**:
- The magnetic field \( B \) generated by an inductor is directly related to the current flowing through it. The energy stored in the magnetic field is given by:
\[ U = \frac{1}{2} L I^2 \]
- Since \( I = 0 \), the magnetic field energy is also:
\[ U = 0 \]
- Therefore, the magnetic field \( B \) is also:
\[ B = 0 \]

4. **Power Delivered by the Battery**:
- The power \( P \) delivered by the battery can be calculated using the formula:
\[ P = V \cdot I \]
- Since \( I = 0 \), the power delivered is:
\[ P = 0 \]

5. **EMF Induced in the Inductor**:
- The induced EMF \( \mathcal{E} \) in the inductor can be calculated using the formula:
\[ \mathcal{E} = -L \frac{di}{dt} \]
- At \( t = 0 \), the current is changing from 0 to some value as time progresses. Therefore, \( \frac{di}{dt} \) is not zero, which means:
\[ \mathcal{E} \neq 0 \]

### Conclusion:
The quantity that is **not zero just after the connection** is the **EMF induced in the inductor**. All other quantities (current, magnetic field, and power delivered) are zero at \( t = 0 \).

### Summary of Results:
- Current \( I = 0 \)
- Magnetic Field \( B = 0 \)
- Power \( P = 0 \)
- EMF Induced \( \mathcal{E} \neq 0 \)