1.You make a capacitor by rolling up a sandwich of two metal films separated by

Question

1.You make a capacitor by rolling up a sandwich of two metal films separated by a 0.01 mm thick insulator. The insulator has a permittivity 10,000,000 times that of air. The capacitor area is 20x500 cm. You place 100 volts on the capacitor. What is the energy stored in kWh? (A kWh is equivalent to 1000 watts or 1000 joules/second running for one hour.)

2.You actually could hook a voltage source up directly to a capacitor, because voltage sources always have an internal resistance that is unavoidable and governed by the connections inside, etc. For the capacitor of problem 1, assuming the 100 volt source has an internal resistance of 1 ohm, how long does it take for the capacitor to charge to 90 volts?

Explanation / Answer

1. find C :

C = keo A / d = 1x10^7 x 8.85 x 10^-12 x (0.2x5) / 0.01x10^-3

=> C = 8.85 F

so energy stored is :

E = 1/2 C V^2 = 0.5 (8.85) (100) = 442.5 J

E = 442.5 Ws = 0.4425 KWs = (0.4425 / 3600) KWh = 1.23 x 10^-4 KWh

___________________________________________________________

2. the time constant T = RC = 1 (8.85) = 8.85 s

so

Vc(t) = 100 (1 - e^-t/8.85 ) V

so 90 = 100 (1 - e^-t/8.85 )

=> 1 - e^-t/8.85 = 0.9

=> e^-t/8.85 = 0.1

ln both sides :

=> -t / 8.85 = -2.3

=> t = 20.378 s

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