For a sinusoidal signal across a resistor, which expression correctly relates output power to peak-to-peak voltage Vpp and resistance R?

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Multiple Choice

For a sinusoidal signal across a resistor, which expression correctly relates output power to peak-to-peak voltage Vpp and resistance R?

When a sinusoidal voltage drives a resistor, the average power depends on the RMS value of the voltage. For a sine wave, the peak-to-peak voltage is twice the peak amplitude, Vpp = 2Vpeak, so Vpeak = Vpp/2. The RMS value is V_rms = Vpeak/√2 = Vpp/(2√2). The average power dissipated in a resistor is P = V_rms^2 / R. Plugging in the rms expression gives P = [Vpp/(2√2)]^2 / R = Vpp^2/(8R). This matches the correct relation. The other options use incorrect RMS conversions for a sine wave, which is why they don’t fit.

When a sinusoidal voltage drives a resistor, the average power depends on the RMS value of the voltage. For a sine wave, the peak-to-peak voltage is twice the peak amplitude, Vpp = 2Vpeak, so Vpeak = Vpp/2. The RMS value is V_rms = Vpeak/√2 = Vpp/(2√2). The average power dissipated in a resistor is P = V_rms^2 / R. Plugging in the rms expression gives P = [Vpp/(2√2)]^2 / R = Vpp^2/(8R). This matches the correct relation. The other options use incorrect RMS conversions for a sine wave, which is why they don’t fit.

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