For a sine wave with a peak value of 230 volts, what is the average value?

For a sine wave with a peak value of 230 volts, what is the average value?

• A. 115 V
• B. 230 V
• C. 146.3 V
• D. 182 V

Answer: (C)

When we talk about the average value of a sine wave in circuit contexts, we usually mean the mean value of the positive half-cycle (the DC component you’d get after rectification). For a sine with peak value Vp, the average over one positive half-cycle is (1/π) ∫0^π Vp sinθ dθ = (2/π)Vp. So with a peak of 230 V, the average over the positive half-cycle is (2/π) × 230 ≈ 460/π ≈ 146.3 V. That’s why the correct value is about 146.3 V. The full-cycle average would be zero because the positive and negative halves cancel, which isn’t what’s being asked here.

When we talk about the average value of a sine wave in circuit contexts, we usually mean the mean value of the positive half-cycle (the DC component you’d get after rectification). For a sine with peak value Vp, the average over one positive half-cycle is (1/π) ∫0^π Vp sinθ dθ = (2/π)Vp.

So with a peak of 230 V, the average over the positive half-cycle is (2/π) × 230 ≈ 460/π ≈ 146.3 V. That’s why the correct value is about 146.3 V. The full-cycle average would be zero because the positive and negative halves cancel, which isn’t what’s being asked here.