Which relation expresses V_peak in terms of V_RMS for a sine wave?

Get ready for the FCC General Radiotelephone Operator License (GROL) exam. Study with flashcards and multiple choice questions, each with hints and detailed explanations. Prepare effectively for your licensing test!

Multiple Choice

Which relation expresses V_peak in terms of V_RMS for a sine wave?

For a sine wave, the RMS value is the effective voltage that would produce the same heating in a resistor. If v(t) = V_peak sin(ωt), then V_RMS = sqrt((1/T) ∫0^T [V_peak sin(ωt)]^2 dt) = V_peak / √2, because the average value of sin^2 over a cycle is 1/2. Rearranging gives V_peak = √2 × V_RMS. This is why the peak value is about 1.414 times the RMS value for a sine wave. The other forms would imply incorrect scaling or inversion (for example, RMS larger than peak or equal to peak), which doesn’t hold for a sine wave.

For a sine wave, the RMS value is the effective voltage that would produce the same heating in a resistor. If v(t) = V_peak sin(ωt), then V_RMS = sqrt((1/T) ∫0^T [V_peak sin(ωt)]^2 dt) = V_peak / √2, because the average value of sin^2 over a cycle is 1/2. Rearranging gives V_peak = √2 × V_RMS. This is why the peak value is about 1.414 times the RMS value for a sine wave.

The other forms would imply incorrect scaling or inversion (for example, RMS larger than peak or equal to peak), which doesn’t hold for a sine wave.

More practice questions