An a.c. of frequency f is flowing in a circuit containing only an ideal choke coil of inductance L. If `V_(0) and l_(0)` represent peak values of the voltage and the current respectively. The average power given by the source to the choke coil is equal to

Options

A. `(1)/(2)l_(0)V_(0)`
B. `(1)/(2)l_(0)^(2) (2pifL)`
C. Zero
D. `(1)/(2)V_(0) (2pifL)`

Answer

To solve the problem, we need to analyze the behavior of an ideal choke coil (inductor) in an alternating current (AC) circuit. Here's a step-by-step solution:

### Step 1: Understand the Circuit Components
An ideal choke coil is a type of inductor that has no resistance. This means that it does not dissipate energy as heat, which is a key characteristic of real-world components that have resistance.

**Hint:** Recall that an ideal inductor only stores energy and does not convert electrical energy into heat.

### Step 2: Analyze Power in AC Circuits
In an AC circuit, the power consumed can be calculated using the formula:
\[ P = V_{\text{rms}} \cdot I_{\text{rms}} \cdot \cos(\phi) \]
where \( \phi \) is the phase difference between the voltage and current.

**Hint:** Remember that the phase difference in an ideal inductor is \( \phi = 90^\circ \), which means \( \cos(90^\circ) = 0 \).

### Step 3: Determine the Average Power
Since the choke coil is ideal, the current lags the voltage by \( 90^\circ \). Therefore, the average power \( P \) delivered to the inductor can be calculated as:
\[ P = V_{\text{rms}} \cdot I_{\text{rms}} \cdot \cos(90^\circ) = 0 \]

**Hint:** Consider what happens to the power formula when the cosine of the phase angle is zero.

### Step 4: Conclusion
Since the average power delivered to the ideal choke coil is zero, we conclude that:
\[ P = 0 \]

Thus, the average power given by the source to the choke coil is equal to zero.

**Final Answer:** The average power given by the source to the choke coil is \( 0 \).