An AC supply gives 30 `underset(rms)(V)` which passes `10 Omega` resistance. The power dissipated in it is

Options

A. 90`sqrt 2` W
B. 90 W
C. 45`sqrt 2` W
D. 45 W

Explanation

To find the power dissipated in a circuit with an AC supply, we can use the formula for power in terms of RMS voltage and resistance. Here’s a step-by-step solution:

### Step-by-Step Solution:

1. **Identify the given values**:
- RMS Voltage (V_rms) = 30 V
- Resistance (R) = 10 Ω

2. **Use the power formula**:
The power dissipated (P) in a resistor when an AC voltage is applied can be calculated using the formula:
\[ P = \frac{V_{rms}^2}{R} \]

3. **Substitute the values into the formula**:
\[ P = \frac{(30 \, \text{V})^2}{10 \, \Omega} \]

4. **Calculate the square of the RMS voltage**:
\[ (30 \, \text{V})^2 = 900 \, \text{V}^2 \]

5. **Divide by the resistance**:
\[ P = \frac{900 \, \text{V}^2}{10 \, \Omega} = 90 \, \text{W} \]

6. **Conclusion**:
The power dissipated in the circuit is **90 Watts**.

### Final Answer:
The power dissipated in the circuit is **90 Watts**.

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