Is it true that a full wave rectifier is more efficient than a half wave and if so why?
In simple terms, in the half-wave rectifier you throw away half of the AC signal by only usiing conduction in one polarity. The advantage is using fewer components (lower cost). The disadvantage is that for a given output voltage the diode must be able to conduct a larger load current (heat).
This is a trick question as stated, IMO. You need to give more context to the question, and give some definition of "efficiency".
If you took efficiency as just power out divided by power in, the half wave rectifier would be slightly more efficient than a bridge rectifier (if we used a bridge rectifier) because the bridge rectifier has two diode voltage drops while the single diode just has one.
Otherwise, there is not a lot of difference because the input power to a half wave rectifier is supplied in half wave bursts and most of this power is delivered to the output.
However if they really meant "how effective are the two methods?", then the full wave bridge circuit would win every time.
The diodes of a bridge rectifier are only conducting half as much current as a half wave rectifier.
The peak current used for charging the filter capacitor is lower because pulses are delivered twice as often.
The filter capacitor can be smaller for the same hum-out level.
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