An alternating current of rms value 10 A is passed through a 12`Omega` resistor. The maximum potential difference across the resistor is

Options

A. 20 V
B. 90 V
C. 169.68 V
D. None of these

Explanation

To find the maximum potential difference across a resistor when an alternating current is passed through it, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Given Values**:
- RMS current (\(I_{\text{RMS}}\)) = 10 A
- Resistance (\(R\)) = 12 Ω

2. **Understand the Relationship**:
The maximum potential difference (\(V_0\)) across a resistor in an AC circuit can be calculated using the formula:
\[ V_0 = I_0 \times R \]
where \(I_0\) is the maximum current. The relationship between the RMS current and the maximum current is:
\[ I_0 = \sqrt{2} \times I_{\text{RMS}} \]

3. **Calculate Maximum Current**:
Substitute the RMS current into the equation to find \(I_0\):
\[ I_0 = \sqrt{2} \times 10 \, \text{A} \approx 1.414 \times 10 \approx 14.14 \, \text{A} \]

4. **Calculate Maximum Potential Difference**:
Now, substitute \(I_0\) and \(R\) into the formula for \(V_0\):
\[ V_0 = I_0 \times R = 14.14 \, \text{A} \times 12 \, \Omega \]
\[ V_0 \approx 169.68 \, \text{V} \]

5. **Final Answer**:
The maximum potential difference across the resistor is approximately **169.68 V**.