What is the average value of an AC voltage whose peak value is 120 volts?

What is the average value of an AC voltage whose peak value is 120 volts?

• A. 76.32 V
• B. 120 V
• C. 60 V
• D. 0.636 V

Answer: (A)

When a voltage is sinusoidal, the average value of its magnitude over a full cycle is 2Vm/π, where Vm is the peak value. This comes from averaging the absolute value of Vm sin(ωt) over one period: (1/2π) ∫0^{2π} |Vm sin θ| dθ = (Vm/π) ∫0^{π} sin θ dθ = 2Vm/π. With Vm = 120 V, the average magnitude is 2×120/π ≈ 240/3.1416 ≈ 76.4 V. This matches the option 76.32 V. So the correct concept is the average value of a sinusoid’s magnitude over a cycle, not the signed average (which would be zero).

When a voltage is sinusoidal, the average value of its magnitude over a full cycle is 2Vm/π, where Vm is the peak value. This comes from averaging the absolute value of Vm sin(ωt) over one period: (1/2π) ∫0^{2π} |Vm sin θ| dθ = (Vm/π) ∫0^{π} sin θ dθ = 2Vm/π.

With Vm = 120 V, the average magnitude is 2×120/π ≈ 240/3.1416 ≈ 76.4 V. This matches the option 76.32 V.

So the correct concept is the average value of a sinusoid’s magnitude over a cycle, not the signed average (which would be zero).