There is an AC source of rms voltage 200 V and frequency 50 Hz. When the source is connected to a circuit then rms current flowing in the circuit is 15 A. Average power delivered by the source

Options

A. is equal to 3000 W.
B. may be 3000 W
C. may be less than 3000 W.
D. may be greater than 3000 W.

Explanation

To find the average power delivered by the AC source, we can use the formula for average power in an AC circuit:

\[ P_{\text{average}} = V_{\text{rms}} \times I_{\text{rms}} \times \cos \phi \]

Where:
- \( P_{\text{average}} \) is the average power,
- \( V_{\text{rms}} \) is the root mean square voltage,
- \( I_{\text{rms}} \) is the root mean square current,
- \( \cos \phi \) is the power factor.

### Step 1: Identify the given values
- \( V_{\text{rms}} = 200 \, \text{V} \)
- \( I_{\text{rms}} = 15 \, \text{A} \)

### Step 2: Calculate the maximum possible average power
Assuming the maximum power factor \( \cos \phi = 1 \) (which occurs under resonance conditions), we can calculate the maximum average power:

\[ P_{\text{average}} = V_{\text{rms}} \times I_{\text{rms}} \times \cos \phi \]

Substituting the values:

\[ P_{\text{average}} = 200 \, \text{V} \times 15 \, \text{A} \times 1 \]

\[ P_{\text{average}} = 3000 \, \text{W} \]

### Step 3: Determine the range of average power
Since the power factor \( \cos \phi \) can vary between 0 and 1, the average power can be less than or equal to 3000 W. Therefore, we can conclude:

\[ P_{\text{average}} \leq 3000 \, \text{W} \]

### Conclusion
The average power delivered by the source can be equal to or less than 3000 W, depending on the value of the power factor \( \cos \phi \).