Only circuit d gives the correct connection of the capacitor to the half-wave rectifier to provide smoothening of the half-wave rectified waveform. Without the capacitor, the halfwave rectifier is connected as shown. The output waveform is attached net to it.
To smooth out the waveform, the capacitor has to be connected parallel to the load as shown below.
During positive cycle, the capacitor is charged to the peak value of the applied ac voltage and then is discharged through R when the applied voltage begins to decrease. The discharge takes place slowly because of the large time-constant. RC and then C become charged to the peak value of the voltage again. The charge-discharge process takes place continuously and so the voltage across the C−R combination is a ripple voltage as shown diagrammatically above. With the C−R arrangement, the average dc voltage is nearly equal to the peak voltage value, which is better, and so the voltage variation.
