To achieve the desired capacitance for your application, you can connect it to different combinations like a series and a parallel combination of a capacitor. Just like resistor combination, the resultant capacitance is bigger or smaller depending upon the connection.

## Capacitors in Series:

Capacitors are called to be connected in series if there is only one path for the flow of current. OR, If the head of the second capacitor is connected to the tail of the first, it is called a series combination as shown in the following circuit.

Apply the KVL to the following circuit will give us

$E=v_{1}+v_{2}+v_{3} \quad \dots(1)$

Where we know that

$v=\frac{Q}{C}$

By putting it to the equation (1), we get

$

\frac{Q_{T}}{C_{T}}=\frac{Q_{1}}{C_{1}}+\frac{Q_{2}}{C_{2}}+\frac{Q_{3}}{C_{3}}

\quad \dots(2)$

There is only one path for current to flow, so the current for series circuit same i.e.

$i_{T}=i_{1}=i_{2}=\ldots =i_{n}$

Multiply the above equation by time t will give us

$i_{T}t=i_{1}t=i_{2}t=\ldots =i_{n}t$

Where, we know from the basic current definition, that

$it=Q$

So

$Q_{T}=Q_{1}=Q_{2}=\ldots =Q_{n} \quad \dots (3)$

Now put it to the equation (2), so we get

$\frac{Q}{C_{T}}=\frac{Q}{C_{1}}+\frac{Q}{C_{2}}+\frac{Q}{C_{3}}$

Dividing the equation by Q

$\frac{1}{C_{T}}=\frac{1}{C_{1}}+\frac{1}{C_{2}}+\frac{1}{C_{3}} \quad \dots (4)$

### capacitors in series summary :

- Provide only one path for charging and discharging current.
- The head of the second capacitor is connected to the tail of the first capacitor.
- The charge of all the capacitors connected in series is the same.
- Adding more capacitors in series will reduce the resultant capacitance.
- The voltage across each capacitor is different.

## The Capacitor in Series Calculator :

Calculate the capacitance with the capacitor in series and parallel calculator. First, put the type of connection and then values of capacitors it will show you the total capacitance either in series connection or in parallel connection.