A sinusoidal voltage has an RMS value of 120 V. What is its peak value approximately?

A sinusoidal voltage has an RMS value of 120 V. What is its peak value approximately?

• A. Approximately 240 V
• B. Approximately 120 V
• C. Approximately 169.7 V
• D. Approximately 84.9 V

Answer: (C)

For a sinusoidal voltage, the peak value is larger than the RMS value by a factor of sqrt(2). The RMS value equals the peak divided by sqrt(2), so to get the peak from the RMS you multiply by sqrt(2). With an RMS of 120 V, the peak is 120 × sqrt(2) ≈ 120 × 1.414 ≈ 169.7 V. So the peak value is about 170 V. The other numbers don’t fit because 240 V would imply a much larger RMS (about 169.7 V), 120 V would mean the peak equals the RMS (not true for a sine), and 84.9 V is 120 divided by sqrt(2), which would correspond to a different RMS.

For a sinusoidal voltage, the peak value is larger than the RMS value by a factor of sqrt(2). The RMS value equals the peak divided by sqrt(2), so to get the peak from the RMS you multiply by sqrt(2). With an RMS of 120 V, the peak is 120 × sqrt(2) ≈ 120 × 1.414 ≈ 169.7 V. So the peak value is about 170 V. The other numbers don’t fit because 240 V would imply a much larger RMS (about 169.7 V), 120 V would mean the peak equals the RMS (not true for a sine), and 84.9 V is 120 divided by sqrt(2), which would correspond to a different RMS.