If Vrms equals 120 V, what is the peak-to-peak voltage?

If Vrms equals 120 V, what is the peak-to-peak voltage?

• A. 339.36V
• B. 120V
• C. 240V
• D. 678.72V

Answer: (A)

For a sine wave, the rms value is the same as the peak value divided by the square root of 2, and the peak-to-peak is twice the peak value. So Vpeak = Vrms × sqrt(2), and Vpp = 2 × Vpeak = 2 × Vrms × sqrt(2). With Vrms = 120 V, Vpp = 2 × 120 × sqrt(2) ≈ 240 × 1.414 ≈ 339.36 V. So the peak-to-peak voltage is about 339.36 V. The other numbers don’t fit the sine relationship: 120 V would be the rms value, not the full swing; 240 V would come from doubling Vrms without accounting for the sqrt(2) factor; 678.72 V is a larger miscalculation from applying an incorrect factor.

For a sine wave, the rms value is the same as the peak value divided by the square root of 2, and the peak-to-peak is twice the peak value. So Vpeak = Vrms × sqrt(2), and Vpp = 2 × Vpeak = 2 × Vrms × sqrt(2).

With Vrms = 120 V, Vpp = 2 × 120 × sqrt(2) ≈ 240 × 1.414 ≈ 339.36 V.

So the peak-to-peak voltage is about 339.36 V.

The other numbers don’t fit the sine relationship: 120 V would be the rms value, not the full swing; 240 V would come from doubling Vrms without accounting for the sqrt(2) factor; 678.72 V is a larger miscalculation from applying an incorrect factor.