Capacitors in Series

       Consider the three capacitors in series connected across the applied voltage V as shown in the Fig. 1. Suppose this pushes charge Q on C₁ then the opposite plate of C₁ must have the same charge. This charge which is negative must have been obtained from the connecting leads by the charge separation which means that the charge on the upper plate of C₂ is also Q. In short, all the three capacitors have the same charge Q.

       

      If an equivalent capacitor stores the same charge, when applied with the same voltage, then it is obvious that,

       It is easy to find V₁, V₂ and V₃ if Q is known.

Note: For all the capacitors in series, the charge on all of them is always same, but the voltage across them is different.

1. Voltage Distribution in Two Capacitors in Series

       Consider two capacitors C₁ and C₂ connected in series. The voltage across them is say, V volts. This is shown in Fig. 2.

      As capacitors are in series, the charge on them is same, say Q.

      Where V₁ is voltage across C₁ and V₂ is voltage across C₂
      Now ,   V = V₁+ V₂
      From the expression of Q, we can write,

The result is exactly identical to the current distribution in two parallel resistances.

 Note : Notice that the smallest capacitor has the largest of the three voltage across it and that C_eq is lesser than any of the capacitors in the series string.

Read also
Capacitors in Parallel