Combination of Capacitors-

 

Before you go through this article, make sure that you have gone through the previous article on Series Combination of Capacitors.

 

We have discussed that capacitors may be connected to each other in the following ways-

 

 

1. Series Combination
2. Parallel Combination
3. Mixed Combination

 

In this article, we will discuss parallel combination of capacitors.

 

Parallel Combination of Capacitors-

 

Two or more capacitors are said to be connected in parallel combination if- the positive plates of all capacitors are connected to one common point and the negative plates to another common point such that the potential difference across each capacitor is same

 

Expression For Equivalent Capacitance-

 

Consider-

• Three capacitors of capacitances C₁, C₂ and C₃ are connected in parallel across a battery.
• The battery maintains a potential difference V across the combination.

 

In parallel combination, the potential difference across each capacitor is same but the total charge drawn from the battery is divided among the individual capacitors.

 

 

In parallel combination, the total charge drawn from the battery is equal to the sum of charges on the individual capacitors i.e.

 

(Equation-01)

 

In steady state, the charge on individual capacitors is given by-

• For 1^st capacitor, Q₁ = C₁V
• For 2^nd capacitor, Q₂ = C₂V
• For 3^rd capacitor, Q₃ = C₃V

 

Using these in Equation-01, we get-

 

(Equation-02)

 

Now, we wish to replace the above parallel combination of capacitors with a single equivalent capacitor.

 

An equivalent capacitor is one which draws the same charge from the battery as drawn by the individual capacitors altogether.

 

Replacing the parallel combination with an equivalent capacitor, we have-

 

 

In steady state, for equivalent capacitor, we have-

 

(Equation-03)

 

On comparing Equation-02 and Equation-03, we get-

 

 

This is the required expression for equivalent capacitance for a parallel combination of capacitors.

The formula can be extended for n capacitors in the same way.

 

In parallel combination, the equivalent capacitance is equal to the sum of individual capacitances.

 

Important Notes-

 

Note-01:

 

In parallel combination,

• The potential difference across each capacitor is same but charge divides among individual the capacitors.
• The total charge drawn from the battery is equal to the sum of charges on the individual capacitors.

 

Note-02:

 

If two capacitors having capacitances C₁ and C₂ are connected in parallel combination, then their equivalent capacitance is given by-

 

 

Note-03:

 

If n capacitors each of capacitance C are connected in parallel combination, then their equivalent capacitance is given by C_eq = C + C + ……… n times. Thus,

 

 

Note-04:

 

In parallel combination, the equivalent capacitance is larger than the largest individual capacitance.

 

Read the next article on-

Energy Stored In A Charged Capacitor

 

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