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An open diode will result in no output from a half wave rectifier, and an open diode will cut the output of a full wave rectifier in half.
You use a half-wave rectifier where the system design does not require a full-wave approach.
Half wave rectifier output is used for running ac motors.
Efficiency is double in case of full wave rectifier.
what is the function of transformer in the half wave rectifier circuit
A clipper can act as a half wave rectifier but it might be a little hard.