why in certain power suplies a capacitor is connected between ground and line at the input?

Answer 1

Power supply decoupling.

This is a noise filter, the effect is to short to ground "high" frequency noise so you have a clean DC supply.

Answer 2

If the power supply is single phase and very large (ten of KW's or much higher) and the cap is also very large, it could be there to reduce electricity bill.

The 110V is the rms voltage of one of the three sinusoidal phases of an AC generator. A purely inductive load of a perfect primary coil of a power supply does not discipitate power but distorts the phase and returns the entire V*A product magnitude. This phase distortion is undesirable and the utility house charges for it because it loads down the generator which tries to keep a 120 degree between any two of the three phases. A well sized capacitor cancels this phase distortion for the most likely load on the secondary coil.

Answer 3

Normally in normal power circuit the inductance are very high which reduces power factor i.e the the ratio of power consumed and billed.The capicitance in the cicuit improves power factor.In some power supply system using a number of Induction motors a Synchonous motor helps in improving PF.The capacitor also used in system where starting load is very high than the running load as in the case of a water pump used for pumping water out of a bore. The charged capacitor discharges energy to meet the starting load requirement.

Answer 4

Although these capacitors can increase the risk of shock hazard, they are used to reduce radio interference.

Answer 5

they are bypass capacitors to pass the noisy signal into the ground..