Question

In a parallel plate capacitor with air between the plates, each plate has an area of 6 × 10–3 m2 and the distance between the plates is 3 mm.Calculate the capacitance of the capacitor. If this capacitor is connected to a 100 V supply, what is the charge on each plate of the capacitor?

Answer 1

Given: The area of each plate of the capacitor is 6× 10 −3   m 2 , dielectric constant of air is 1 and the distance between the plate is 3 mm.

The capacitance of the capacitor is given as,

C= k ε 0 A d

where, capacitance of the capacitor is C, area of each plate is A, permittivity of free space is ε 0 , distance between the parallel plates is d and dielectric constant is k.

For air:

By substituting the given values in the above equation, we get,

C= 1×8.854× 10 −12 ×6× 10 −3 0.003 =17.71× 10 −12  F ≈18 pF

Therefore, the capacitance of the capacitor is 18 pF.

The capacitor is connected to 100 V supply.

The charge on the capacitor is given as,

q=C×V

where, the charge on the capacitor is q, the potential difference of each capacitor is V, and the capacitance of capacitor is C.

By substituting the given values in the above equation, we get,

q=17.71× 10 −12 ×100 ≈1.8× 10 −9  C

Therefore, the charge on each plate of the capacitor is 1.8× 10 −9  C.