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If diode in the bridge circuit becomes open the circuit will become a half wave rectifier instead, but if a diode in a full wave rectifier opens then the whole circuit becomes open. (No current flow).

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The outputs of the bridge and the two-diode full wave rectifier are not the same.

For the rectified voltage to be the same value, the two-diode full wave rectifier must be supplied from a centre tapped transformer winding, the total voltage of which is twice that necessary for the bridge rectifier circuit.

Furthermore, the maximum d.c. which may be drawn from the centre tapped transformer/two-diode arrangement, assuming capacitive filtering, is the same value as the transformer secondary winding's capacity.

In the case of the bridge, the maximum d.c. which may be drawn, also assuming capacitive filtering, is 62% of the transformer secondary winding's capacity.

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Q: Why you are using the bridge rectifier in most of the circuits instead of full wave rectifier eventhough the output of both are same?
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How many diodes in a bridge rectifier?

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