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 (AC) flows through it, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values**:
- RMS current (\(I_{\text{rms}}\)) = 10 A
- Resistance (\(R\)) = 12 Ω

2. **Calculate the maximum current (\(I_0\))**:
The relationship between the RMS current and the maximum current is given by:
\[ I_{\text{rms}} = \frac{I_0}{\sqrt{2}} \]
Rearranging this formula to find \(I_0\):
\[ I_0 = I_{\text{rms}} \times \sqrt{2} \]
Substituting the given RMS current:
\[ I_0 = 10 \, \text{A} \times \sqrt{2} \]
\[ I_0 = 10\sqrt{2} \, \text{A} \]

3. **Calculate the maximum potential difference (\(V_0\))**:
The maximum potential difference across the resistor can be calculated using Ohm's law:
\[ V_0 = I_0 \times R \]
Substituting the values we found:
\[ V_0 = (10\sqrt{2}) \times 12 \]
\[ V_0 = 120\sqrt{2} \, \text{V} \]

4. **Calculate the numerical value of \(V_0\)**:
Now, we need to compute \(120\sqrt{2}\):
\[ V_0 \approx 120 \times 1.414 \approx 169.68 \, \text{V} \]

5. **Conclusion**:
The maximum potential difference across the resistor is approximately \(169.68 \, \text{V}\).

### Final Answer:
The maximum potential difference across the resistor is \(169.68 \, \text{V}\).

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