In an `AC` circuit, the applied potential difference and the current flowing are given by
`V=20sin100t` volt ,`I=5sin(100t-pi/2)` amp
The power consumption is equal to

Options

A. `1000W`
B. `40W`
C. `20W`
D. zero

Explanation

To solve the problem step by step, we need to calculate the power consumption in the given AC circuit using the formulas for RMS voltage and current, as well as the phase difference between them.

### Step 1: Identify the given values
The voltage and current equations are:
- \( V = 20 \sin(100t) \) volts
- \( I = 5 \sin(100t - \frac{\pi}{2}) \) amperes

### Step 2: Determine the peak (maximum) values
From the equations, we can identify:
- Peak voltage, \( V_0 = 20 \) volts
- Peak current, \( I_0 = 5 \) amperes

### Step 3: Calculate the RMS values
The RMS (Root Mean Square) values are calculated using the formula:
- \( V_{rms} = \frac{V_0}{\sqrt{2}} \)
- \( I_{rms} = \frac{I_0}{\sqrt{2}} \)

Calculating these:
- \( V_{rms} = \frac{20}{\sqrt{2}} = 10\sqrt{2} \) volts
- \( I_{rms} = \frac{5}{\sqrt{2}} = \frac{5\sqrt{2}}{2} \) amperes

### Step 4: Determine the phase difference
The phase difference \( \phi \) can be determined from the current equation:
- The current leads the voltage by \( \frac{\pi}{2} \) radians (since \( I \) has a phase shift of \( -\frac{\pi}{2} \)).
- Therefore, \( \phi = \frac{\pi}{2} \).

### Step 5: Calculate the power factor
The power factor \( \cos(\phi) \) is calculated as:
- \( \cos\left(\frac{\pi}{2}\right) = 0 \)

### Step 6: Calculate the power consumption
Using the formula for power consumption in an AC circuit:
- \( P = V_{rms} \cdot I_{rms} \cdot \cos(\phi) \)

Substituting the values:
- \( P = (10\sqrt{2}) \cdot \left(\frac{5\sqrt{2}}{2}\right) \cdot 0 \)
- \( P = 0 \)

### Conclusion
The power consumption in the circuit is \( 0 \) watts.

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