Question

A sinusoidal voltage of rms value 220 V is applied to a
diode and a resistor R in the circuit shown in figure, so
that half wave rectification occurs. If the diode is ideal,
what is the rms voltage across Rı?

(a) 55√2 v
(c) 110 v
(b) 110√2 V
(d) 220√2 V​

Answer 1

Answer:

option D

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Answer 2

Answer:

110V

Explanation:

In a half wave rectifier, the negative half cycle will be removed from the output. So, the total base length(2π) should be taken from the interval 0 to 2π.

The RMS voltage, VRMS = √ Vm2/2π 0∫π sin2ωt dωt

= √ Vm2/2π 0 ∫π(1 – cos2ωt) / 2 ) dωt = √ Vm2/4π [ωt – sin2ωt / 2]0π

= √ Vm2/4π [ π – (sinπ) / 2 – (0 – (sin0) / 2)] = √ Vm2/4π ( π ) = √ Vm2/ 4

Therefore the RMS voltage, VRMS = Vm/ 2

VRMS =220/2=110V