Which quantity is zero when averaging over a full cycle?

Which quantity is zero when averaging over a full cycle?

• A. The average value
• B. The peak value
• C. The RMS value
• D. The peak-to-peak value

Answer: (A)

Over a full cycle, a quantity that is purely alternating and symmetric about zero will have its positive and negative portions cancel out. For a simple AC waveform like v(t) = Vp sin(ωt), the average over one period T is (1/T) ∫_0^T Vp sin(ωt) dt, which equals zero because the integral of sine over a full cycle is zero. The other measurements aren’t zero because they’re not about cancellation. The peak value is the maximum amplitude Vp, so it’s nonzero. The RMS value for a sine wave is Vp/√2, representing the effective heating value, and it is also nonzero. The peak-to-peak value is the difference between the maximum and minimum voltages, which for a sine is 2Vp, also nonzero.

Over a full cycle, a quantity that is purely alternating and symmetric about zero will have its positive and negative portions cancel out. For a simple AC waveform like v(t) = Vp sin(ωt), the average over one period T is (1/T) ∫_0^T Vp sin(ωt) dt, which equals zero because the integral of sine over a full cycle is zero.

The other measurements aren’t zero because they’re not about cancellation. The peak value is the maximum amplitude Vp, so it’s nonzero. The RMS value for a sine wave is Vp/√2, representing the effective heating value, and it is also nonzero. The peak-to-peak value is the difference between the maximum and minimum voltages, which for a sine is 2Vp, also nonzero.