A circular parallel plate capacitor with plate radius 5cm has an electric field

Question

A circular parallel plate capacitor with plate radius 5cm has an electric field between the plates of E(t) = 10N/C exp(-t/10s). Compute the displacement current as a function of time. Open-Response Homework Problem 13.4 A coil of resistance 12Ohm and self-inductance 2mH is connected across an ideal 12V battery. (a) Compute the time constant. (b) Sketch the current through the inductor as a function of time. (c) How long does it take for the current in the circuit to reach 99% of its final value? (d) How much energy is stored in the inductor when the final current is reached?

Explanation / Answer

13.3)

displacement current Id = eo*(d/dt)*phi

electric flux = E*A = 10*e^-(t/10)*pi*r^2

Id = -eo*10*pi*r^2*e^-(t/10)*(-1/10)

Id = -8.84*10^-12*10*pi*0.05^2*(1/10)*e^-(t/10)

Id = -6.94*10^-14*e^-(t/10)

13.4)

time constant T = L/R = 2*10^-3/12 = 1.67*10^-4 s

(b)

(c)

i = I*(1-e^-(t/T))

i = 0.99 I

0.99 = (1-e^-(t/(1.67*10^-4)))

t = 0.000769 s

(d)

energy U = (1/2)*L*I^2

I = V?R = 12/12= 1A

U = (1/2)*2*10^-3*1^2

U = 0.001 J

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