# Capacitance

## Effect of Dielectric

- Dielectric are non conducting materials for ex- Glass,mica,wood etc.

- What happened when space between the two plates of the capacitor is filled by a dielectric was first discovered by faraday.

- Faraday discovered that if the space between conductors of the capacitor is occupied by the dielectric,the capacitance of capacitor is increased.

- If the dielectric completely fills the space between the conductors of the capacitor ,the capacitance is increased by an factor K which is characterstics of the dielectric and This factor is known as the dielectric constan.

- Dielectric constant of vaccum is unity.

- Consider a capacitor of capacitance C
_{0} is being charged by the connecting it to a battery.

- If Q
_{0} is the amount of charged on the capacitor at the end of the charging and V_{0} is potental diffrence across the plates of the capacitor then

C_{0}=Q_{0} /V_{0} ----(17)

Thus charge being placed on the capacitor is

Q_{0}=C_{0}V_{0}

- If the battery is diconnected and space between the capacitor is filled by a dielectric the P.D decrease to a new value

V=V_{0}/K.

- Since the original charge is still on the capacitor,the new capacitance will be

C=Q_{0}/V=KQ_{0}/V_{0}=KC_{0}----(19)

- From equation 19 it follows that C is greater then C
_{0}.

- Again if the dielectric is inserted while the battery is still connected then battery would have to supply some amount of charge to maintain the P.D between the plates and then total charge on the plates would be Q=KQ
_{0}.

- In either of the cases ,capacitance of the capacitor is increase by the amount K.

- For a parallel plate capacitor with dielectric of dielectric constant K between its plates its capacitance becomes

C=εA/D ----(20)

where ε=Kε_{0}

- When a sufficiently strong electric field is applied to any dielectric material it becomes a conductor and this phenomenon is known as dielectric breakdown.

- The maximun electric field a material can withstand without the occurence of breakdown is called dielectric strength of that material.

- Thus field across the capacitor should never exceed breakdown limits in order to store charge on capacitor without leaking.

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