current through the smoothing capacitor in bridge rectifier
The transformer can only supply current to the load while the transformer voltage is above the capacitor voltage. At all other times the capacitor supplies current to the load.

Since all power ultimately has to come from the transformer and the diodes only conduct part of the time then the current pulses will be many times that of the average load current.



Figure 1. The half-wave rectifier version of the waveforms. The green current waveform has been superimposed on the original graph.

See my answer to Interpreting the ripple curve of a half wave rectifier which discuses the same question for a half-wave rectifier.