What is the peak value of 65 volts RMS?

What is the peak value of 65 volts RMS?

• A. 91.94 V
• B. 65 V
• C. 46.0 V
• D. 130 V

Answer: (A)

For a sine wave, the RMS value is the peak value divided by sqrt(2). So the peak value equals the RMS value times sqrt(2). With 65 V RMS, the peak is 65 × sqrt(2) ≈ 65 × 1.41421356 ≈ 91.92 V, which rounds to 91.94 V. That’s why 91.94 V is the correct peak value. The other numbers come from mixing up the conversion: 65 V is the RMS itself, not the peak; 46.0 V would be 65 divided by sqrt(2), which would be the RMS if the peak were 65 V; and 130 V would be 2 × 65, which uses a factor of 2 instead of sqrt(2).

For a sine wave, the RMS value is the peak value divided by sqrt(2). So the peak value equals the RMS value times sqrt(2). With 65 V RMS, the peak is 65 × sqrt(2) ≈ 65 × 1.41421356 ≈ 91.92 V, which rounds to 91.94 V. That’s why 91.94 V is the correct peak value.

The other numbers come from mixing up the conversion: 65 V is the RMS itself, not the peak; 46.0 V would be 65 divided by sqrt(2), which would be the RMS if the peak were 65 V; and 130 V would be 2 × 65, which uses a factor of 2 instead of sqrt(2).