Assertion : Peak value of current in `AC` through a resistance of `10 Omega` is `2 A`. Then, power consumed by the resistance should be `20 W`.
Reason : Power in `AC` is `P=I_("rms")^2R`

Options

A. If both Assertion and Reason are true and the Reason is correct explanation of the Assertion.
B. If both Assertion and Reason are true but Reason is not the correct explanation of Assertion
C. If Assertion is true, but the Reason is false.
D. If Assertion is false but the Reason is true.

Explanation

To solve the problem, we will analyze the assertion and reason provided in the question step-by-step.

### Step 1: Understand the Assertion
The assertion states that the peak value of the current (I₀) in an AC circuit through a resistance of 10 ohms is 2 A. We need to determine if the power consumed by the resistance is indeed 20 W.

### Step 2: Calculate RMS Current
The RMS (Root Mean Square) value of the current (I_rms) can be calculated from the peak current (I₀) using the formula:
\[ I_{rms} = \frac{I_0}{\sqrt{2}} \]
Substituting the given peak current:
\[ I_{rms} = \frac{2 \, \text{A}}{\sqrt{2}} = \frac{2}{1.414} \approx 1.414 \, \text{A} \]

### Step 3: Use the Power Formula
The power consumed by the resistor (P) can be calculated using the formula:
\[ P = I_{rms}^2 \cdot R \]
Substituting the values we have:
\[ P = (1.414 \, \text{A})^2 \cdot 10 \, \Omega \]
Calculating \( (1.414)^2 \):
\[ (1.414)^2 \approx 2 \]
Thus:
\[ P \approx 2 \cdot 10 = 20 \, \text{W} \]

### Step 4: Conclusion
The assertion is correct as the power consumed by the resistance is indeed 20 W. The reason provided, which states the formula for power in AC circuits, is also correct. Therefore, both the assertion and reason are true, and the reason correctly explains the assertion.

### Final Answer
Both the assertion and reason are true, and the reason is the correct explanation of the assertion.

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