In an AC series circuit, the instanctaneous current is zero when the instantaneous voltage is xamimum. Connected to the source may be a

Options

A. pure capacitor
B. pure inductor
C. combination of pure an inductor and pure capacitor
D. pure resistor

Answer

To solve the question regarding the AC series circuit where the instantaneous current is zero when the instantaneous voltage is maximum, we will analyze each option provided in the question systematically.

### Step-by-Step Solution:

1. **Understanding the Problem**:
- We need to identify which component (pure capacitor, pure inductor, combination of both, or pure resistor) satisfies the condition that the instantaneous current is zero when the instantaneous voltage is at its maximum.

2. **Analyzing Pure Capacitor**:
- In a pure capacitor, the phase difference between voltage and current is \( \phi = \frac{\pi}{2} \) (90 degrees).
- This means that the voltage leads the current by 90 degrees.
- When the current is maximum, the voltage is zero, and when the current is zero, the voltage is maximum.
- **Conclusion**: The condition is satisfied for a pure capacitor.

3. **Analyzing Pure Inductor**:
- In a pure inductor, the phase difference is also \( \phi = \frac{\pi}{2} \).
- However, in this case, the voltage lags the current by 90 degrees.
- Therefore, when the current is maximum, the voltage is zero, and when the current is zero, the voltage is maximum.
- **Conclusion**: The condition is satisfied for a pure inductor as well.

4. **Analyzing Combination of Pure Inductor and Pure Capacitor**:
- For a combination of pure inductor and pure capacitor, the phase difference can be expressed as \( \phi = \tan^{-1}\left(\frac{X_L - X_C}{R}\right) \).
- In the case of pure inductor and pure capacitor (where resistance \( R = 0 \)), the phase difference becomes \( \phi = \frac{\pi}{2} \).
- This means that the behavior is similar to both pure inductor and pure capacitor, where the voltage and current relationship holds.
- **Conclusion**: The condition is satisfied for the combination of pure inductor and pure capacitor.

5. **Analyzing Pure Resistor**:
- In a pure resistor, the phase difference is \( \phi = 0 \).
- This means that the voltage and current are in phase; they reach their maximum and minimum values at the same time.
- Therefore, the condition that the instantaneous current is zero when the instantaneous voltage is maximum is not satisfied.
- **Conclusion**: The condition is not satisfied for a pure resistor.

### Final Answer:
The components that satisfy the condition are:
- Pure Capacitor
- Pure Inductor
- Combination of Pure Inductor and Pure Capacitor