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If the input is pulsating DC, then the output will be pulsating DC. It will not be shaped the same, but it will be close, depending on the frequency and rise and fall time in comparison with the inductive reactance of the transformer.
To smooth the output of the pulsating DC.
voltage regulator is a component to convert pulsating DC into constant DC.
A "Rectifier" converts AC current to pulsating DC current.
A: As a DC source change state rapidly this variation is consider an AC component