Question

Obtain an expression for equivalent capacitance when three capacitors C1, C2 and C3 are connected in series.

Answer 1

Hint: We know that a capacitor is nothing but a device used to store an electric charge, consisting of one or more pairs of conductors separated by an insulator. Named these capacitors as C1, C2, and C3 write those expressions and finally we consider 3 capacitors are replaced by a single capacitor to obtain a required answer.

Complete answer:

Let three capacitors C1, C2 and C3 are connected in series. We know charge remains the same in the series combination.
$\eqalign{
  & {V_1} = \dfrac{q}{{{C_1}}} \cr
  & {V_2} = \dfrac{q}{{{C_2}}} \cr
  & {V_3} = \dfrac{q}{{{C_3}}} \cr} $
When we placed these in serious combination then we have
$\eqalign{
  & \Rightarrow V = {V_1} + {V_2} + {V_3} \cr
  & \Rightarrow V = q\left( {\dfrac{1}{{{C_1}}} + \dfrac{1}{{{C_2}}} + \dfrac{1}{{{C_3}}}} \right) \cr} $
when we 3 capacitors are replaced by a single capacitor such that on giving it charge q is capacitance is C then we have
$V = \dfrac{q}{C}$
Then above equation become
$\therefore \dfrac{q}{C} = q\left( {\dfrac{1}{{{C_1}}} + \dfrac{1}{{{C_2}}} + \dfrac{1}{{{C_3}}}} \right)$
Hence we obtain the equation for equivalent capacitance when three capacitors are connected in series.

Additional information:
$\bullet$ We need to know what a capacitor is? A capacitor is a passive electronic component that stores energy in the form of an electrostatic field. In other words, a capacitor consists of two conducting plates separated by an insulating material called the dielectric.
$\bullet$ Some students may confuse capacitance, remember it is just the effect of a capacitor is known as capacitance. While some capacitance exists between any two electrical conductors in proximity in a circuit a capacitor is a component which is designed to add capacitance to a circuit.

Note:
If we want, we can cancel q on both sides in the obtained expression. Capacitors are the essential components of an electronic circuit, without a capacitor the circuit cannot be completed. The use of capacitors includes smoothing the ripples from AC in the power supply, coupling and decoupling the signals.