Find the average power consumed in the circuit consisting of resistanceless inductor .

Answer

To find the average power consumed in a circuit consisting of a resistanceless inductor, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Circuit**:
- The circuit consists of a pure inductor, which means it has no resistance (R = 0).

2. **Formula for Average Power**:
- The average power (P) consumed in an AC circuit can be calculated using the formula:
\[ P = V \times I \times \cos \phi \]
- Here, \(V\) is the voltage, \(I\) is the current, and \(\cos \phi\) is the power factor.

3. **Determine the Power Factor**:
- The power factor \(\cos \phi\) is defined as:
\[ \cos \phi = \frac{R}{Z} \]
- In this case, since the circuit is a pure inductor, the resistance \(R = 0\).

4. **Calculate the Power Factor**:
- Substituting \(R = 0\) into the power factor formula gives:
\[ \cos \phi = \frac{0}{Z} = 0 \]

5. **Substitute into the Average Power Formula**:
- Now substitute \(\cos \phi = 0\) into the average power formula:
\[ P = V \times I \times 0 = 0 \]

6. **Conclusion**:
- Therefore, the average power consumed in a circuit consisting of a resistanceless inductor is:
\[ P = 0 \]

### Final Answer:
The average power consumed in the circuit consisting of a resistanceless inductor is **0 watts**.

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