Capacitors, Series And Parallel Combination, Important Topics For JEE 2024

Capacitors : We know that a capacitor is a device that stores electrical energy. In this article, we will discuss the equivalent capacitance when we connect a number of capacitors in series and parallel.

Concept Of Capacitance

Concept Of Capacitance : The measure of ability of ability of a conductor to store charge on it is the capacitance of the conductor. The potential of a conductor increases when conductor is charged. The increase in potential is directly proportional to the charge given to the conductor.

Here, the constant C is known as the capacitance of the conductor. It is a scalar quantity with SI unit coulomb/volt or farad and dimension

Capacitance Of An Isolated Spherical Conductor

Capacitance Of An Isolated Spherical Conductor : Consider on amount of charge Q is given to an isolated spherical conductor of radius R . Then, the potential at the surface of sphere is

If the conductor is placed in a medium then the capacitance,

Capacitor Or Condenser

Capacitor : A capacitor or condenser is a device that stores electric energy. It is a pair of two conductors of any shape, which is close to each other and have equal and opposite charge.

Capacitance of a capacitor is defined as the magnitude of charge Q on the positive plate divided by the magnitude of the potential difference V between the plates.

When a battery is connected across the plates, a capacitor gets charged. The flow of charge carrier stop in the circuit once capacitor gets fully charged. Then the potential difference across the capacitor will be same as the potential difference across the terminals of the battery.

When we speak about the charge Q on a capacitor, we are referring to the magnitude of the charge on each plate but the net charge on the capacitor is always zero.

Series Combination Of Capacitors

Series Combination Of Capacitors : Consider three capacitors of capacitance C ₁ , C ₂ and C ₃ are connected in series. V ₁ , V ₂ and V ₃ are the potential across them, respectively.

We know that, and

Also,

If

If there are ‘ n ’ identical capacitors,

Energy stored in the combination

Parallel Combination Of Capacitors

Parallel Combination Of Capacitors : Consider three capacitor of capacitance C ₁ , C ₂ and C ₃ are connected in parallel. Q ₁ , Q ₂ and Q ₃ are the charge on the capacitor C ₁ , C ₂ and C ₃ respectively. All three capacitor will have same potential.

We know that, and

Also,

If

If there are ‘ n ’ identical capacitors,

Energy stored in the combination,

Capacitor Example

Example 1 : In the circuit diagram shown in the adjoining figure, the resultant capacitance between P and Q is

A. 47 μ F

B. 3 μ F

C. 60 μ F

D. 10 μ F

Sol. The given circuit can be drawn as where

Example 2: The resultant capacitance between A and B in the following figure is equal to

A. 1 μ F

B. 3 μ F

C. 2 μ F

D. 1.5 μ F

Sol. The given circuit can be redrawn as follows

On further solving the network in similar manner equivalent capacitance obtained between A and B will be 1 μ F .