The average American household uses about 100 million Joules (MJ) of energy per

Question

The average American household uses about 100 million Joules (MJ) of energy per day. If you were to make a circular-parallel plate capacitor with spacing of d = 5 mm (air gap), what would the radius of the plates have to be in order to store 100 MJ of energy if a potential difference of Delta V = 1000V is maintained across the plates? (b) Disconnect the voltage source and insert a piece of dielectric material with _r = 5 to fill the region between the plates. Describe quantitatively how the following quantities change: C, Q, Delta V, E_net - field, and U.

Explanation / Answer

a)

energy

U = 0.5 C V^2

100 x 10^6 J = 0.5 C x ( 1000x1000)

C = 200 F

epsilon A / d = 200

A = 1.12994 x 10^11 m^2

A = pi x r x r

r = 189650.25 m

b)

Q will not change

C becomes 5 times

Voltage becomes 1/5 times

E becomes 1/5 times

Energy becomes 1/5 times

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