Question

Question 1: Consider a sheet of paper with a thickness of 0.1 mm and a dielectric constant of 3. Suppose we would like to make a 1 F capacitor using this sheet as a spacer between two metallic plates. What should be the area of the sheet?

Suppose we took a 1 F capacitor from problem 1 and attached a 1V battery to it. After the charging was complete the battery was disconnected.

Question 2: What is the charge on the capacitor?

Question 3: How much work did the battery produce?

Question 4: What is the total energy of the capacitor after charging?

Answer 1

Question 1 -

For the metallic plates capacitor,

Gap between the plates, d = 0.1 mm = 0.1 x 10^-3 m

Dielectric constant of the medium between the plates, k = 3

Area of the plates, A = ?

Capacitance of the capacitor, C = 1 F

Expression for the capacitance of a parallel plates capacitor,

C = (k**A) / d --------------------------------------------(i)

where, = 8.854 x 10^-12 F/m

So, from equation (i) -

1 = ( 3 x 8.854 x 10^-12 * A) / (0.1 x 10^-3)

=> A = (0.1 x 10^-3) / (3 x 8.854 x 10^-12) = 3.76 x 10^-3 x 10^9 = 3.76 x 10^6 m^2 (Answer)

Question 2 -

Charge on the capacitor, Q = C x V = 1 x 1 = 1 Coulomb. (Answer)

Question 3 -

Work produced by the battery, W = (1/2)*C*V^2

= 0.5*1*1^2 = 0.5 J (Answer)

Question 4 -

Total energy of the capacitor = work produced by the battery = 0.5 J (Answer)