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Question

The maximum efficiency of full-wave rectifier is


A

100%

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B

25.20%

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C

42.2%

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D

81.2%

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Solution

The correct option is D

81.2%


Step 1: Given

A full-wave rectifier is given. Its efficiency is η.

Step 2: Formula Used

A full wave rectifier converts AC (alternating current) voltage into DC voltage (direct current). The efficiency of the full wave rectifier can be calculated by finding the percentage of the ratio of DC power PDC to AC power PAC. Thus, the efficiency is given by η=PDCPAC×100%.

The power of the DC circuit is PDC=VDC2RL, where VDC=2VMπ is voltage in the DC circuit, VM is peak voltage and RL is load resistance.

The power of the AC circuit is PAC=VRMS2RL, where VRMS=VM2 is root mean square voltage in the AC circuit, VM is peak voltage and RL is load resistance.

Step 3: Calculate the Efficiency

Substitute all the expressions in the efficiency formula.

η=PDCPAC×100%=VDC2RLVRMS2RL×100%=VDC2VRMS2×100%

Further substitute VDC=2VMπ and VRMS=VM2.

η=VDC2VRMS2×100%=2VMπ2VM22×100%=22π2×100%=8π2×100%=81.2%

Hence, the maximum efficiency of a full-wave rectifier is 81.2%.


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