Capacitors in Series

The equations for calculating capacitors in Series, and for calculating the voltage across each capacitor, is on the right. You might note that the equations for capacitance are similar to resistors in Parallel. While capacitors in Parallel are simply added together (see the section below), whereas capacitors in Series require a more complicated equation.

The resultant of two capacitors in Series can be calculated using the top equation. For three, or more, capacitors, the second equation needs to be used. Enter your capacitor values at the top of the diagram, under C₁, C₂, and C₃, and then click outside the box to find C_T for the capacitors in Series. If you only wish to calculate the resultant value of two capacitors, leave one of the boxes empty or enter 0.

The relationship of the voltages across each capacitor is shown in the Voltage equations. For each capacitor in series, the voltage across a particular capacitor is equal to the Total Capacitance (C_T) divided by the capacitance of the capacitor, which is then multiplied by the Total Voltage (E_XY). Entering a voltage in the box marked E_XY, and then clicking outside the box, will mark the voltages across each capacitor.

Capacitors in Parallel

On the left is the equation for capacitors in parallel. The total, C_T, is the sum of all the values in parallel. The drawing to the right can be used to illustrate that fact.

In the areas provided, enter your capacitor values for C₁, C₂, and C₃, and then click outside the box, to find C_T for the capacitors in Parallel. If you only wish to calculate the resultant value of two capacitors, leave one of the boxes empty or enter 0.

Capacitors in Series/Parallel

C1 = µF	C2 = µF
C3 = µF	C4 = µF
Voltage (each Capacitor) = VDC
Total Voltage X to Y = VDC
X Y + C1 50.0 uF @ 200.0 V + C2 50.0 uF @ 200.0 V R1 22 KΩ R2 22 KΩ + C3 50.0 uF @ 200.0 V + C4 50.0 uF @ 200.0 V 50.0 uF @ 400.0 V

It's common to run into a problem where you have capacitors of the correct capacitance, but the voltage rating is only 1/2 of the voltage required. If you have extra capacitors of the same value, you can use four capacitor in a Series/Parallel arrangement to obtain a voltage rating that meets your requirements. To insure that the capacitors share the applied voltage properly, it is common to place a balancing resistor, 100 Ω per volt, across each parallel pair.

For example, say you have bunch of 50µF capacitors rated at 200 Volts DC, but want to use them on a power supply that requires capacitors with a 400 Volts DC rating. Four of these capacitors, in a Series/Parallel arrangement, will provide you with 50µF @ 400 Volts DC. In this case, the resistors values would be 20KΩ (100Ω*200V=20,000Ω). That is assuming a maximum of 200 V DC across each capacitor. Probably, a common 22KΩ 10% resistor would be usable. With 22KΩ resistors across each capacitor pair, and 200 Volts DC across them, the current would be 9.091 mA and the power would be 1.82 Watts. 5 Watt resistors would be needed to be safe.

Some Quick Things To Remember About Capacitors In Series

1. The resultant value is always less than the lowest capacitor.
2. If the capacitors are of equal value, the resultant value is equal to the value of one of the capacitors, divided by the number of capacitors. For example, if there are three 100 pF capacitors in series the resultant value will be 100/3 = 33.333 pF.
3. If a very large capacitor and a very small capacitor are in series, the resultant value will only be a little bit less then the smaller capacitor. For example, if there are a 10,000 pF capacitor in parallel with a 100 pF capacitor the resultant value will be 99 pF. Just 1 pF less than the lower value capacitor. Not very practical.

Note: There are many instances of having small value capacitors in parallel with large value capacitors. Most commonly, this is seen in power supplies. For example, you might see a 0.1µF ceramic capacitor in parallel with a 500µF Electrolytic capacitor (0.1µF + 500µF = 500.1µF). This is done to exploite the physical properties of the different capacitor types, rather than adjust the value. In the example, the 500µF Electrolytic might be intended to help smooth low frequency ripple. While the 0.1µF is meant for high frequency noise suppression.