Capacitor

A capacitor is a passive device that can store an electrical charge on its plates when connected to a voltage source. It is a device that stores electrical energy in the form of an electric field. It is a passive electronic device with its two terminals.

The effect of a capacitor is also known as capacitance. Capacitance also exists between any two electrical conductors in closeness in a circuit, a capacitor is an integrant originate to add capacitance to a circuit. The capacitor was firstly known as a condenser or condensator.

Capacitor consists of two electrical conductors separated by a distance. If the space between capacitors is a vacuum then it is also known as a vacuum capacitor. Although if space is filled with an insulating material known as a dielectric capacitor. The amount of charge storage in a capacitor is determined by a property called capacitance.

Capacitor Formula

Let a Electric Flux \phi of a uniform electric field “E” passing through perpendicularly of an imaginary flat surface of area “A” is can be written as

\phi =EA

For a small charge Q and spherical surface encircle the charge, the flux is found by noting that is perpendicular to the surface at all points

\phi =EA

\phi =\frac { Q }{ 4\pi r^2 } 4\pi r^2

\phi =\frac { Q }{ \epsilon_0 }

Let the plates are separated by a distance d then

V=Ed

or E=\frac { V }{ d }

Integrating on both side

EA=\frac { V }{ d }A

=\frac { Q }{ \epsilon_0 }

Q=(\frac { \epsilon_0 A }{ d })V

By comparing this equation with the charge equation

Q=CV

then C=\frac { \epsilon_0 A }{ d }

C is inversely proportional to the distance “d” between them and directly proportional to the area “A” of the plates.

Series Combination Of Capacitor

Let two capacitors C_1 and C_2 are connected in series with a battery of voltage V. The capacitors C_1 and C_2 gain the same unknown charge.

two capacitor connected in series

Unknown voltage across the capacitor C_1 and C_2 are

V_1=\frac { Q }{ C_1 } and V_2=\frac { Q }{ C_2 }

Voltage V=V_1+V_2 = Q\left( \frac { 1 }{ C_1 } +\frac { 1 }{ C_2 } \right)

Q=\left( \frac { 1 }{ C_1 } +\frac { 1 }{ C_2 } \right)^{-1}V=C_{eq}V

C_{eq}=\left( \frac { 1 }{ C_1 } +\frac { 1 }{ C_2 } \right)^{-1}

\frac { 1 }{ C_{eq} } =\frac { 1 }{ C_1 } +\frac { 1 }{ C_2 }

C_{eq}=\frac { C_1C_2 }{ C_1+C_2 }

We can easily find the voltage across the each capacitor

V_1=\frac {C_2 }{ C_1+C_2 }V and V_2=\frac { C_1 }{ C_1+C_2 }V

Parallel Combination Of Capacitor

Let two capacitors C_1 and C_2 are connected in parallel with a battery of voltage V. The capacitors C_1 and C_2 gain the same unknown charge.

two capacitor connected in parallel

charge on capacitor is Q_1=C_1V and Q_2=C_2V

The total charge stored in the this circuit is Q=Q_1+Q_2

Q=(C_1+C_2)V= C_{eq}V

C_{eq}=C_1+C_2

The equivalent capacitance of the circuit is the sum of capacitances in the circuit.

What happens when a conductor is placed in an electric field ?

Consider a conductor is placed in an electric field, between the parallel plates of a capacitor.

As we know that the conductor contains free charges i.e. electrons, they move towards the positive plate, making the surface of the conductor closer to the positive plate of the capacitor negatively charged this process is called induced charges.

As we know that the conductor contains free charges i.e. electrons, they move towards the positive plate, making the surface of the conductor closer to the positive plate of the capacitor negatively charged this process is called induced charges.

The surface of the conductor at the end closer to the negative plate is positively charged. The motion of charges continues until the internal electric field created by induced charges cancel the external field and making the field inside the conductor zero.

The surface of the conductor at the end closer to the negative plate is positively charged. The motion of charges continues until the internal electric field created by induced charges cancel the external field and making the field inside the conductor zero.

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