Question

The basic reason why a full-wave rectifier has a twice the efficiency
of a half-wave rectifier is that: (A) it makes use of transformer (B) the
heating loss is much less (C) it utilizes both half-cycles of the input
(D ) its output frequency is double the line frequency

Answer 1

(C) it utilizes both half-cycles of the input.

Brief explanation: a full-wave rectifier conducts on both positive and negative half-cycles, so the DC component of the output and the delivered DC power are much larger than for a half-wave rectifier. For a sinusoidal input:

- Half-wave: Vdc = Vm/π, Vrms = Vm/2 ⇒ η = (Vdc/Vrms)^2 = 4/π^2 ≈ 0.405 (40.5%)
- Full-wave: Vdc = 2Vm/π, Vrms = Vm/√2 ⇒ η = 8/π^2 ≈ 0.811 (81.1%)

Thus the full-wave efficiency is about twice that of the half-wave. (The doubled output frequency in option D is a consequence, not the basic reason.)