## Capacitors in Series

##### Posted on : Sun , 01 2014 by : virusi

## Theory of operation :

In series capacitors will each have the same amount of charge stored on them because the charge from the first one travels to the second one and so on.
We can remove the charge (Q) from the equation (2):
Equation 3 can be overwritten :
Or
Using the formula (3) or (4) we can calculate the total capacitance for a certain number of capacitors. As you can see capacitance is similar to resistance in parallel so the same tips and tricks from resistors in parallel can be used.

Fig.1 Capacitors in series

The voltage of the circuit is spread out amongst the capacitors (so each capacitor gets a potion of the total voltage).
\large V_{T} = V_{1} + V_{2} + V_{3}+...+V_{n}(1)

We already know that is the voltage across the ideal capacitor (

V = \frac{Q}{C}) :

\large \frac{Q}{C_{T}} = \frac{Q}{C_{1}} + \frac{Q}{C_{2}} + \frac{Q}{C_{3}} + ... + \frac{Q}{C_{n}}(2)

\large \frac{1}{C_{T}} = \frac{1}{C_{1}} + \frac{1}{C_{2}} + \frac{1}{C_{3}} + ... + \frac{1}{C_{n}}(3)

\large C_{T} = \frac{1}{\frac{1}{C_{1}}} + \frac{1}{\frac{1}{C_{2}}} + \frac{1}{\frac{1}{C_{3}}} + ... + \frac{1}{\frac{1}{C_{n}}}(4)

\large C_{T} = \frac{C_{1}*C_{2}*C_{3}*...*C_{n}}{C_{1}+C_{2}+C_{3}+...+C_{n}}(5)

## Practical Example :

If you don’t see the example below than you should follow this steps:

– In your browser allow Java SE 7.

– Lower you java security settings (Go to Control Panel >> Java >> Security and set the security level to medium) .

– Edit Site List (Go to Control Panel >> Java >> Security and click on Edit Site List… and add eagerlearning.org in the list).

This is a very simple circuit with 2 resistors, 3 capacitors and 2 switches. If you want to charge the capacitors than the 1 switch should be closed and the 2 switch should be opened. If you want to discharge the capacitors than you should close the 2 switch and open the 1 switch. The charge time depends on the R1 resistance and the discharge time depends on the resistance R2 so if you want your capacitors to charge/discharge faster than you should put a smaller resistance or vice versa if you want your capacitor to charger/discharge slower. The diagrams are showing the current and voltage that are flowing through the capacitors. If you want to change the value of a component just double click on it and insert the desired value.
Last updated on Mon , 03 2014

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