Capacitors in Parallel

Let three capacitors C₁ , C₂ and C₃  be connected in parallel as shown. The capacitor plates are named  A,B,C,D,E and F.

When a battery is connected to the parallel combination, the –ve terminal of the battry supplies a charge –Q which gets divided into –Q₁ , –Q₂  and  –Q₃  , in direct proportion to capacitance values, to get stored on plates B, D and F respectively. Simultaneously, the +ve terminal of the battery sucks charge  –Q₁ , –Q₂  and  –Q₃   from plates A, C and E respectively and therefore creating +ve charges  Q₁ , Q₂  and  Q₃  on plates A,C and E respectively. Thus, charge is conserved.

So now, plates A, C and E have +Q₁ ,+Q₂  and + Q₃ and plates  B, D and F  have -Q₁ ,-Q₂  and -Q₃  charges respectively.

The above process continues till the capacitors are fully charged and potential difference across each of them becomes V.

In steady state,

Q₁ = C₁V

Q₂ = C₂V

Q₃ = C₃V

But, by law of conservation of charge  i.e Kirchhoff's current law

Q = Q₁ + Q₂ + Q₃  

∴   Q = C₁ V+ C₂ V + C₃ V                     ...(1)

Lets replace the parallel combination by a single capacitor C_eq such that the single capacitor will store the same amount of charge Q on application of same potential difference V.

Then,          Q=C_eqV                                ...(2)

Equating (1) and (2)

C_eqV = C₁ V+ C₂ V + C₃ V

So, equivalent capacitance for a parallel combination of capacitances is given by the formula

To summarise :-

1. All capacitors connected in parallel have same potential difference across them for any value of capacitances.
2. Equivalent capacitance value is greater than all the individual capacitance values.
3. Equivalent capacitance formula is given by

           C_eq = C₁ + C₂ + C₃ 
  4.   As potential difference is same across all the capacitors in parallel,           therefore
           Q ∝ C 

                i.e higher the capacitance value, higher the charge stored on the                capacitor and vice-versa.

Related Concepts :-
 (1) Capacitors in Series