Q. 534.0( 2 Votes )

# A parallel-plate capacitor of capacitance 5 μF is connected to a battery of emf 6V. The separation between the plates is 2 mm.

a) Find the charge on the positive plate.

b) Find the electric field between the plates.

c) A dielectric slab of thickness 1 mm and dielectric constant 5 is inserted into the gap to occupy the lower half of it. Find the capacitance of the new combination.

d) How much charge has flown through the battery after the slab is inserted?

Answer :

Given-

Capacitance C=5 μF = F

Voltage, V=6v

Separation between plates, d=2 mm=2×10^{-3} m

a)The charge on the positive plate is calculated using

*q* = c×v

where, c is the capacitance

and v = voltage applied

Thus,

q=5 μF×6 V

=30 μC

b) The electric field between the plates of the capacitor is given by

Where, v is the applied voltage and d is the distance between the capacitor plates

⇒

=3×10^{3} V/m

c)Given-

Distance between the plates of the capacitor, *d* =2×10^{-3} m

Dielectric constant of the dielectric material inserted, *k* = 5

Thickness of the dielectric material inserted, *t* = 1×10^{-3} m

capacitance of the capacitor= 5 μF

Now,

To calculate area of the plates of the capacitor,

Where,

A = area

k = dielectric constant of the material placed

d= separation between the plates

substituting the values,

When the dielectric placed in it, the capacitance becomes

t=thickness of the material

substituting the values,

1)

d)

The charge stored in the capacitor initially is -

C=5×10^{-6} F

Also, V=6 V

Now, we know

where v is the applied voltage and c is the capacitance

⇒

⇒

Now, when the dielectric slab is inserted ,charge on the capacitor, from 1)

Charge, Q’

Now, charge flow is given by,

Rate this question :

A parallel-plate capacitor has plate area 20 cm^{2}, plate separation 1.0 mm and a dielectric slab of dielectric constant 5.0 filling up the space between the plates. This capacitor is joined to a battery of emf 6.0 V through a 100 kΩ resistor. Find the energy for the capacitor 8.9 μs after the connections are made.

How many time constants will elapse before the energy stored in the capacitor reaches half of its equilibrium value in a charging RC circuit?

HC Verma - Concepts of Physics Part 2