In the calculations above, we didn't take the ESR of the capacitor into account. However, the ESR plays an important role in power supplies due to the large charge and discharge currents. The ripple voltage will increase by at least I∙ESR. This will be in the case where the capacitor can be fully charged. However, that will never be the case. Calculating the ripple voltage for a certain ESR is not an easy task. Since we often do not know the exact ESR value of a capacitor, we'd better use computer simpulation to view the results of a certain ESR:
C = 4700uF; ESR = 0Ω
C = 4700uF; ESR = 1Ω
The frequency of the (non-rectified) input signal is 50Hz. The discharge current is 0.5A.
The first image shows the situation whithout ESR. The ripple voltage is about 0.9V. On the right, the output voltage is plotted when the ESR is 1Ω. The ripple voltage is now 1.8V! So the ESR added 0.9V to the ripple voltage.
Let's see what happens if, due to aging, the ESR increases to 3Ω.
The ripple voltage has now grown to 3V. In audio applications, a heavily aged supply capacitor can be heard as a 100Hz humm.
If computer simulation shows that the ESR has to be impossibly small, you may connect multiple capacitors in parallel:
This image shows the situation with two 2200uF capacitors each having an ESR of 1Ω. Although the total capacitance is less, the ripple voltage is less than the situation with one 4700uF capacitor: just 1.3V. The increase of the ripple voltage (due to ESR) has dropped from 0.9V to 0.4V. This is one of the reasons you'll often see parallel-connected capacitors in power supplies. (Another reason may be that there are no capacitors available with a higher capacitance.)