In an A.C. circuit, the current flowing in inductance is `I = 5 sin (100 t – pi//2)` amperes and the potential difference is `V = 200 sin (100 t)` volts. The power consumption is equal to

Options

A. 1000 watt
B. 40 watt
C. 20 watt
D. Zero

Explanation

To solve the problem, we will follow these steps:

### Step 1: Identify the given values
We have the following equations for current and voltage in the AC circuit:
- Current: \( I = 5 \sin(100t - \frac{\pi}{2}) \) A
- Voltage: \( V = 200 \sin(100t) \) V

### Step 2: Calculate the RMS values of current and voltage
The RMS (Root Mean Square) values for sinusoidal waveforms are given by:
- \( I_{rms} = \frac{I_{max}}{\sqrt{2}} \)
- \( V_{rms} = \frac{V_{max}}{\sqrt{2}} \)

From the current equation, the maximum current \( I_{max} = 5 \) A.
From the voltage equation, the maximum voltage \( V_{max} = 200 \) V.

Calculating the RMS values:
- \( I_{rms} = \frac{5}{\sqrt{2}} \)
- \( V_{rms} = \frac{200}{\sqrt{2}} \)

### Step 3: Determine the phase difference \( \phi \)
The phase difference \( \phi \) between the current and voltage can be determined from their equations:
- The voltage \( V \) has a phase of \( 0 \).
- The current \( I \) has a phase of \( -\frac{\pi}{2} \).

Thus, the phase difference \( \phi \) is:
\[ \phi = 0 - \left(-\frac{\pi}{2}\right) = \frac{\pi}{2} \]

### Step 4: Calculate the power factor
The power factor \( \cos \phi \) is given by:
\[ \cos \phi = \cos\left(\frac{\pi}{2}\right) = 0 \]

### Step 5: Calculate the power consumption
The power consumption \( P \) in an AC circuit is given by:
\[ P = V_{rms} \cdot I_{rms} \cdot \cos \phi \]

Substituting the values we calculated:
\[ P = \left(\frac{200}{\sqrt{2}}\right) \cdot \left(\frac{5}{\sqrt{2}}\right) \cdot 0 \]
\[ P = 0 \]

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

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