A parallel-plate capacitor is made of two 20 cm times 3.0 cm sheets of aluminum

Question

A parallel-plate capacitor is made of two 20 cm times 3.0 cm sheets of aluminum foil, which separated by stuck of paper 1.0 mm thick. a) What is the capacitance of the capacitor made this wav if the dielectric constant of the paper is 3.7? (epsilon_0 = 8.85 times 10^-12 C^2/N times m^2) b) What is the charge on each plate if 12-V battery is connected across the two plates? c) What is the electric field (E) between the plates? d) Calculate how much electric energy can be stored in this stored in this capacitor if it was connected for long time to a 12-V battery.

Explanation / Answer

given

the paper stuck delectric constant k = 3.77

A = 20 X 3 = 60 cm2 = 60 X 10-4 m2

d = 1 mm = 10-3 m

a )

C = k o A / d

C = 3.77 X 8.85 X 10-12 X 60 X 10-4 / 10-3

C = 1.998 X 10-12 F

C = 0.53 pF

b )

V = 12 volts

Q = C X V

Q = 1.998 X 10-12 X 12

Q = 2.39 X 10-11 C

c )

V = E d

E = V / d

E = 12 / 10-3

E = 12 X 103 volts

d )

U = 1/2 C V2

U = 0.5 X 1.998 X 10-12 X 122

U = 1.43 X 10-10 J

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