The average power is dissipated in a pure inductor is

Options

A. `(VI^(2))/4`
B. `1/2VI`
C. zero
D. `VI^(2)`

Explanation

To solve the question regarding the average power dissipated in a pure inductor, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Circuit**: In a pure inductive circuit, the current lags behind the voltage by 90 degrees (or π/2 radians). This is a fundamental characteristic of inductors in AC circuits.

2. **Identifying the Phase Difference**: The phase difference (φ) between the voltage and current in a pure inductor is given as:
\[ \phi = 90^\circ \]

3. **Using the Power Formula**: The average power (P) in an AC circuit can be calculated using the formula:
\[ P = V_{\text{rms}} I_{\text{rms}} \cos \phi \]
where \( V_{\text{rms}} \) is the root mean square voltage, \( I_{\text{rms}} \) is the root mean square current, and \( \cos \phi \) is the cosine of the phase difference.

4. **Calculating Cosine of the Phase Difference**: Since we have a phase difference of 90 degrees:
\[ \cos 90^\circ = 0 \]

5. **Substituting into the Power Formula**: Now substituting the value of \( \cos \phi \) into the power formula:
\[ P = V_{\text{rms}} I_{\text{rms}} \cdot 0 = 0 \]

6. **Conclusion**: Therefore, the average power dissipated in a pure inductor is:
\[ P = 0 \]

### Final Answer:
The average power dissipated in a pure inductor is **0**.