Obtain an expression for effective Capacitance of two Capacitors Connected in series.

Explanation

Capacitors are said to be connected in series when (a) Same charge appears in each of them (b) Voltage divides in the inverse ratio of their Statement: The reciprocal of the equivalent capacitance of a number of capacitors connected in series is equal to the algebraic sum of the reciprocals of their individual capacitances. capacitances.
ie., `V=V_1 +V_2`, and `C=Q/V`,so that `V =Q/C`
hence `Q/C=Q/C_1 + Q/C_2`
i.e., `1/C=1/C_1 +1/C_2`
For .. unidentical capacitances,
`1/C=1/C_1 + 1/C_2 + 1/C_3` + .........+ `1/C_n`
Statement : The reciprocal of the equivalent capacitance in series is equal to the algebraic sum of the reciprocals of their individual capacitances .
Note: (a) For .n identical capacitors `C_S=C/n`
(b) For 3 unidentical capacitors,
`1/C=1/C_1 + 1/C_2 + 1/C_3`