A parallel plate capacitor is made from circular plates of Aluminum foil each wi

Question

A parallel plate capacitor is made from circular plates of Aluminum foil each
with a radius of 3cm. The distance between the plates is 8 mm. A 120V EMF is connected to the plates.

a) Find the charge stored in this capacitor.

b) Calculate the amount of energy stored in the capacitor.

c) If one were to keep the 120V battery connected while increasing the separation between the plates to 12mm, what would be the final energy stored in the capacitor?

d) If instead one disconnects the battery and increases the distance between the plates to 12mm, what would be the final energy stored in the capacitor?

Explanation / Answer

a.

C = A / d = ( (3 cm)2) / (8 mm) = 3.13 x 10-12 F

Q = CV = (3.13 x 10-12 F)(120 V) = 3.76 × 10-10 C

b.

U = (1/2)CV2 = (1/2)(3.13 x 10-12 F)(120 V)2 = 2.25 × 10-8 J

c.

C = A / d = ( (3 cm)2) / (12 mm) = 2.09 x 10-12 F

Since the capacitor remains hooked up to the battery, V remains constant; however, the charge and capitance decrease.

U = (1/2)CV2 = (1/2)(2.09 x 10-12 F)(120 V)2 = 1.50 × 10-8 J

d.

Since the battery is disconnected, the charge on the capacitor remains constant.

U = Q2 / (2C) = (3.76 × 10-10 C)2 / (2(2.09 x 10-12 F)) = 3.38 x 10-8 J

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