Electrical Engineering ⇒ Topic : Capacitors in Series

Capacitors in Series

Consider three capacitors, having capacitances C₁, C₂ and C₃ farad respectively, connected in series across a p.d. of V volts [See Fig.  (i)]. In series connection, charge on each capacitor is the *same (i . e . +Q on one plate and -Q on the other) but p.d. across each is different

                                                              figure (a)

But Q/V is the **total capacitance C_T between points A and B so that  V/Q = 1/C_T [See Fig.(ii)].

Thus capacitors in series are treated in the same manner as are resistors in parallel.

Special Case. Frequently we come across two capacitors in series. The total capacitance in such a case is given by ;

Note. The capacitors are connected in series when the circuIt voltage exceeds the voltage rating of individual units. In using the series connection, it is important to keep in mind that the voltages across capacitors in series are not the same unless the capacitances are equal. The greater voltage will be across the smaller capacitance which may result in its failure if the capacitances differ very much.

CAPACITORS IN SERIES

The series connection of three capacitors is shown in Figure (a).

Let C_1, C₂, and C₃ be the capacitances of the three capacitors, respectively. V₁, V₂, and V₃ be the potential differences across the three capacitors.

In series combination, the charge on each capacitor is same but the potential difference is different.

                                           figure (a)

For n capacitors in series, it can be written as follows:

Figure  shows the arrangement of capacitors C₁, C₂ and C₃ in series. The right hand plate of the first capacitors is connected to the left hand plate of the second one and the right hand plate of the second one to the left hand plate of the third. Finally all the three capacitors are connected in series to the battery supply providing the emf across the points A and D.

A charge q passes through each capacitor since there is only one path through which charge can pass. The potential difference across each capacitor is different and is given by

From the circuit , it is seen that the sum of the three voltages,

                                       equation(a)

If C is the equivalent capacitance of the three capacitors in series, then

                                                                   equation (b)

    Therefore, from Equation(a) and (b), we get

Thus, in general, if n capacitors of value C₁, C₂, C₃, .... C_n are connected in series, their equivalent capacitance is given as

It can be seen from the above equation that when capacitors are connected in series, the equivalent capacitance is always less than any individual capacitance in the circuit. Equations (a) and (b) derived for capacitors are exactly opposite to equations obtained for resistors when connected in parallel and in series.