What is the purpose of a filter in a rectifier circuit?

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With an AC current the voltage varies from positive to negative (say +- 115 volts for US wall current). If you hooked it up to a oscilloscope it would look like a sine wave. True DC looks like a flat line. Devices that need DC voltage want that voltage to be steady. When you rectify AC through a bridge, the unfiltered voltage looks like AC only with all the negative arcs flipped to the positive side, so the potential bounces between the desired voltage and zero (picture the path of a bouncing ball). The capacitor smooths the current to more closely match true DC.

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Filter would reduce the sharp surges in the circuit

my grandson wants the answer to this?/?

Usually, there is a filter capacitor in a full wave rectifier circuit to get rid of the AC noise on the DC voltage. There is always a little ripple after rectification, and a cap will get rid of a lot of it.
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