120 V AC voltage is applied to 10 ohm resistance. The peak voltage across the resistor is

Options

A. 120 V
B. `120 sqrt2V`
C. `(120)/(sqrt2) V`
D. none of these

Explanation

To find the peak voltage across a resistor when a 120 V AC voltage is applied, we can follow these steps:

### Step 1: Understand the relationship between RMS voltage and peak voltage
The root mean square (RMS) voltage (V_rms) is related to the peak voltage (V_peak) in an AC circuit by the formula:
\[ V_{peak} = V_{rms} \times \sqrt{2} \]

### Step 2: Identify the given values
From the problem statement, we know:
- The RMS voltage (V_rms) applied is 120 V.

### Step 3: Calculate the peak voltage
Using the formula from Step 1, we can substitute the known value:
\[ V_{peak} = 120 \, V \times \sqrt{2} \]

### Step 4: Simplify the calculation
Calculating the peak voltage:
\[ V_{peak} = 120 \times 1.414 \] (approximately, since \(\sqrt{2} \approx 1.414\))
\[ V_{peak} \approx 169.68 \, V \]

### Step 5: Final answer
Thus, the peak voltage across the resistor is approximately:
\[ V_{peak} \approx 169.68 \, V \]

### Summary of the Solution
The peak voltage across the resistor when a 120 V AC voltage is applied is approximately 169.68 V.

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