What is the peak-to-peak voltage of a sine wave with an RMS voltage of 120 volts?

The peak-to-peak voltage of a sine wave can be calculated from its RMS (Root Mean Square) voltage using the relationship between these two values. For a sine wave, the RMS voltage is equal to the peak voltage divided by the square root of 2, or mathematically, ( V_{RMS} = \frac{V_{peak}}{\sqrt{2}} ).

To find the peak voltage from the RMS voltage of 120 volts, you can rearrange the formula:

1. Multiply both sides by ( \sqrt{2} ): ( V_{peak} = V_{RMS} \times \sqrt{2} )

2. Substituting the RMS voltage into the formula gives: ( V_{peak} = 120 , \text{volts} \times \sqrt{2} )

Using the approximate value of ( \sqrt{2} ) (about 1.414), you get: ( V_{peak} \approx 120 \times 1.414 \approx 169.68 , \text{volts} ).

The peak-to-peak voltage is then twice the peak voltage, calculated as: ( V_{pp}