Consider a series RC circuit as in the figure below for which R = 3.00 MOhm, C =

Question

Consider a series RC circuit as in the figure below for which R = 3.00 MOhm, C = 4.00 muF, and epsilon = 34.0 V. (a) Find the time constant of the circuit. (b)What is the maximum charge on the capacitor after the switch is thrown closed? (c)Find the current in the resistor 10.0 s after the switch is closed. A 2.00-nF capacitor with an initial charge of 5.61 muC is discharged through a 1.88-kOhm resistor. (a)Calculate the current in the resistor 9.00 mus after the resistor is connected across the terminals of the capacitor. (Let the positive direction of the current be define such that dQ/dt > 0.) (b)What charge remains on the capacitor after 8.00 mus? (c)What is the (magnitude of the) maximum current in the resistor?

Explanation / Answer

a)

Time constant is given as

T = RC = 3 x 106 x 4 x 10-6 = 12 sec

b)

Qmax = CV = (4 x 10-6 ) (34) = 136 uC

c)

Voltage across the capacitor after 10 sec is given as

V(10) = V (1 - e-t/T)

V(10) = 34 (1 - e^(-10/12))

V(10) = 19.22 volts

voltage across the resistor = Vr = 34 - 19.22 = 14.78 volts

i = current = Vr /R = 14.78 / (3 x 106) = 4.93 uA

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