Explain the need of a filter in mobile phone adapter

 A mobile phone adapter or charger is a low voltage DC power supply.

It rectifies AC main supply to a pulsating DC which is not directly usable.

A cell phone like any other electronic circuit requires some thing closer to pure DC as produced by batteries. Unlike pure DC waveform of a battery , a rectifier output has an AC ripple riding on the DC waveform.

The circuit used in a DC power supply to remove the ripples is called as a FILTER.

A filter circuit can produce a very smooth waveform that approximates the waveform produced by a battery. The most common technique used for filtering is a capacitor connected across the output of a rectifier.