In an `AC` circuit, the current is given by `i=5sin(100t-(pi)/2)` and the `AC` potential is `V=200sin(100)`volt. Then the power consumption is

Options

A. `20` watt
B. `40` watt
C. `1000` watt
D. `0` watt

Explanation

To solve the problem of power consumption in the given AC circuit, we will follow these steps:

### Step 1: Identify the given values
The current \( i \) and voltage \( V \) are given as:
- Current: \( i = 5 \sin(100t - \frac{\pi}{2}) \)
- Voltage: \( V = 200 \sin(100t) \)

### Step 2: Determine the peak values of current and voltage
From the equations:
- The peak current \( I_{\text{peak}} = 5 \, \text{A} \)
- The peak voltage \( V_{\text{peak}} = 200 \, \text{V} \)

### Step 3: Calculate the RMS values
The RMS (Root Mean Square) values are calculated using the formula:
\[ V_{\text{rms}} = \frac{V_{\text{peak}}}{\sqrt{2}} \quad \text{and} \quad I_{\text{rms}} = \frac{I_{\text{peak}}}{\sqrt{2}} \]
Calculating these:
\[ V_{\text{rms}} = \frac{200}{\sqrt{2}} \quad \text{and} \quad I_{\text{rms}} = \frac{5}{\sqrt{2}} \]

### Step 4: Find the phase difference \( \phi \)
The phase difference \( \phi \) between the voltage and the current can be determined from the equations:
- The current lags the voltage by \( \frac{\pi}{2} \) radians (or 90 degrees).

### Step 5: Calculate the power consumption
The power consumption \( P \) in an AC circuit is given by the formula:
\[ P = V_{\text{rms}} \cdot I_{\text{rms}} \cdot \cos(\phi) \]
Substituting the values we found:
- \( \cos(\phi) = \cos\left(\frac{\pi}{2}\right) = 0 \)

Thus, the power consumption becomes:
\[ P = \left(\frac{200}{\sqrt{2}}\right) \cdot \left(\frac{5}{\sqrt{2}}\right) \cdot 0 = 0 \, \text{W} \]

### Conclusion
The power consumption in the circuit is \( 0 \, \text{W} \).

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