Q. 68

# A parallel-plate

Answer :

Energy stored in a capacitor:

The energy stored in a capacitor with capacitance C , charge is given by:

where V is the potential difference across the capacitor.

Capacitance of a Capacitor in presence of a dielectric:

The capacitance of the capacitor is initially C_{0} and then a dielectric medium of dielectric constant K is inserted between the plates. The new capacitance is

Also for parallel plate capacitors,

Where ϵ_{0} is the permittivity of free space, A is the area of plate and l is the distance between the plates.

Charging a capacitor:

A capacitor of capacitance C is being charged using a battery of emf ϵ through a resistance R . A switch S is also connected in series with the capacitor. The switch is initially open. The capacitor is uncharged at first. At t=0, the switch is closed. The current through the circuit at anytime t>0 is given by:

Where I_{0} is the initial current.

The charge is given by:

Note that is known as time constant.

Given,

Area of the plate,

(

Now, distance of separation:

Dielectric constant,

Emf of battery,

Resistance ,

Time,

Now,

Time constant,

We want to find the charge on the capacitor at t = 8.9μs

Now, energy of the capacitor is given by:

Hence, the capacitor stores of energy after 8.9μs.

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