If in a circuit lags behind EMF by `pi//2` . Then it is a/an

Options

A. resistor circuit
B. capacitor
C. inductor circuit
D. CR circuit

Explanation

To determine the type of circuit in which the current lags behind the electromotive force (EMF) by \( \frac{\pi}{2} \), we can analyze the behavior of different circuit components: resistors, inductors, and capacitors.

### Step-by-Step Solution:

1. **Understanding Phase Relationship**:
- In an AC circuit, the relationship between current (I) and voltage (V) can be described in terms of phase angles. If the current lags behind the voltage, it means that the voltage reaches its peak before the current does.

2. **Resistor Behavior**:
- In a purely resistive circuit, the current and voltage are in phase. Therefore, the phase difference is 0. This is not the case here since the current lags.

3. **Inductor Behavior**:
- In a purely inductive circuit, the voltage leads the current by \( \frac{\pi}{2} \) (or 90 degrees). This means that if the voltage is at its maximum, the current is at zero. Thus, the current lags behind the voltage by \( \frac{\pi}{2} \).
- Mathematically, if the voltage across an inductor is given by \( V = V_0 \sin(\omega t) \), the current can be expressed as \( I = I_0 \sin\left(\omega t - \frac{\pi}{2}\right) \), indicating that the current lags the voltage by \( \frac{\pi}{2} \).

4. **Capacitor Behavior**:
- In a purely capacitive circuit, the current leads the voltage by \( \frac{\pi}{2} \). This means that the current reaches its peak before the voltage does, which is opposite to the behavior we are analyzing.

5. **Conclusion**:
- Since the current lags behind the EMF by \( \frac{\pi}{2} \), this indicates that the circuit is purely inductive.

### Final Answer:
The circuit is an **inductive circuit**.

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