Rectifier Average Voltage
Calculate the average (DC) voltage of a full-wave rectifier, V_dc = 2 × V_p ÷ π, from the peak voltage V_p of the sinusoidal input. The result, in volts, is the mean value of the pulsating voltage at the rectifier output before filtering — about 63.7% of the peak. A full-wave rectifier (bridge or center-tap) flips the negative half-cycles, doubling the ripple frequency and raising the average voltage compared with a half-wave rectifier (V_p/π). It is the basis of designing DC power supplies from the AC mains. Capacitor filtering then raises the voltage further (close to the peak). Enter the peak voltage.
Result
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Average voltage of a full-wave rectifier
The first stage of almost every power supply fed from the mains (alternating current) is rectification: turning the AC, which swings between positive and negative, into a voltage that always keeps the same sign (pulsating, but positive only). A full-wave rectifier (either a four-diode bridge or a centre-tapped transformer) does this by flipping the negative half-cycles upward, so the output is a train of positive humps. The average voltage (the DC value a DC voltmeter would read) of that waveform is V_dc = 2 × V_p ÷ π ≈ 0.637 × V_p, where V_p is the peak voltage of the incoming sine wave. In other words, the average sits at roughly 64% of the peak. Compare it with the half-wave rectifier (a single diode, which throws the negative half-cycles away): its average is only V_p/π ≈ 0.318·V_p — half the full-wave figure. That is why the full-wave rectifier is nearly always preferred: it uses both half-cycles, delivers twice the average voltage and, importantly, doubles the ripple frequency (from 60 to 120 Hz on the Brazilian grid), which makes the filtering that follows easier and more effective. After rectification comes the filter capacitor, which charges up close to the peak and holds the voltage between humps — so the final DC voltage of the supply (with a filter) lands near V_p, not at the average, which describes the unfiltered case. This average voltage is the starting point for designing linear supplies and the front end of switch-mode supplies. Enter the peak voltage.
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