Energy loss in pure capacitance in A.C. circuit is-

Options

A. `(1)/(2) CV^(2)`
B. CV
C. `(1)/(4)CV^(2)`
D. Zero

Answer

To solve the question regarding energy loss in pure capacitance in an AC circuit, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the AC Circuit with Pure Capacitance**:
- In an AC circuit that consists purely of a capacitor, the capacitor is connected to an AC voltage source.

2. **Power in AC Circuits**:
- The power (P) in an AC circuit can be expressed using the formula:
\[ P = V_{\text{rms}} \cdot I_{\text{rms}} \cdot \cos \phi \]
where:
- \( V_{\text{rms}} \) is the root mean square voltage,
- \( I_{\text{rms}} \) is the root mean square current,
- \( \phi \) is the phase difference between the voltage and the current.

3. **Phase Difference in Pure Capacitance**:
- In a pure capacitive circuit, the current leads the voltage by 90 degrees. Thus, the phase angle \( \phi \) is 90 degrees.

4. **Calculating Power**:
- The cosine of 90 degrees is:
\[ \cos 90^\circ = 0 \]
- Substituting this value into the power formula gives:
\[ P = V_{\text{rms}} \cdot I_{\text{rms}} \cdot \cos 90^\circ = V_{\text{rms}} \cdot I_{\text{rms}} \cdot 0 = 0 \]

5. **Conclusion**:
- Since the power is zero, it indicates that there is no energy loss in a pure capacitive AC circuit. Therefore, the energy loss in pure capacitance in an AC circuit is zero.

### Final Answer:
The energy loss in pure capacitance in an AC circuit is **zero**.

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