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

Options

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

Answer

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

### Step 1: Understand the relationship between RMS current and maximum current
The root mean square (RMS) value of current (I_RMS) is related to the maximum current (I_0) by the formula:
\[ I_0 = \sqrt{2} \times I_{RMS} \]

### Step 2: Substitute the given RMS value
Given that the RMS value of the current is 10 A, we can substitute this value into the formula:
\[ I_0 = \sqrt{2} \times 10 \, A \]

### Step 3: Calculate the maximum current
Calculating this gives:
\[ I_0 = \sqrt{2} \times 10 \approx 1.414 \times 10 \approx 14.14 \, A \]

### Step 4: Use Ohm's law to find the maximum potential difference
The maximum potential difference (V_0) across the resistor can be calculated using Ohm's law:
\[ V_0 = I_0 \times R \]
where R is the resistance of the resistor.

### Step 5: Substitute the resistance value
Given that the resistance R is 12 Ω, we substitute this value into the equation:
\[ V_0 = 14.14 \, A \times 12 \, \Omega \]

### Step 6: Calculate the maximum potential difference
Calculating this gives:
\[ V_0 = 14.14 \times 12 \approx 169.68 \, V \]

### Final Answer
Thus, the maximum potential difference across the resistor is approximately **169.68 V**.

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