Skip to main content

Average and RMS of rectified wave

Short answer

The half-wave pulse train has period 2π, peak 10 V. Average over full period: Vav = 10/π ≈ 3.18 V. RMS value: Vrms = Vm/2 = 5 V.

Calculate the (i) average value and (ii) RMS value of voltage wave shown in figure below: [Figure: half-wave pulses of sinusoidal shape with peak 10 V, positive half cycles from 0 to π and from 2π to 3π with gaps in between, period T = 2π.]

From the figure: sinusoidal half-wave pulses of peak Vm = 10 V, one in 0 to π, the next in 2π to 3π. The voltage is zero from π to 2π. Time period T = 2π.

i) Average value over one period

Vav = (1/2π) ∫₀^π 10 sin θ dθ = (10/2π) [−cos θ]₀^π = (10/2π)(2) = 10/π

Vav = 3.18 V

(If the average is taken only over the conducting half-cycle 0 to π, it is 2Vm/π = 6.37 V. For the periodic wave shown, with T = 2π, the average is 3.18 V.)

ii) RMS value

Vrms² = (1/2π) ∫₀^π (10 sin θ)² dθ = (100/2π) ∫₀^π (1 − cos 2θ)/2 dθ

= (100/2π) × (π/2) = 25

Vrms = √25 = 5 V (that is, Vm/2)

Answer: Vav = 3.18 V, Vrms = 5 V.

✓ Answer checked by Claude Opus 5.5 (high effort)

Related questions

All Basic Electrical Engineering chapter 5 questions →