In an RC series circuit EMF = 120.0 V, R = 1.40 M Ohm, and C = 1.80 mu F. (a) Ca

Question

In an RC series circuit EMF = 120.0 V, R = 1.40 M Ohm, and C = 1.80 mu F. (a) Calculate the time constant, (b) Find the maximum charge that will appear on the capacitor during charging, (c) How long does it take for the charge to build up to 20 mu C? (d) What is the maximum current through the resistor? (e) What is the potential difference across the capacitor after it has been charging for 0.1 sec? (f) Sketch the charge and current as functions of time, (g) After being totally charged, the capacitor is carefully disconnected from the circuit above without discharging it. It is connected to a 520 k Ohm resistor and begins to discharge. What is the time constant for this circuit? (h) What will be the potential difference across the capacitor after 400 msec? Sketch the charge and current as functions of time.

Explanation / Answer

(A) Time constant = R C = 1.40 x 10^6 x 1.80 x 10^-6 = 2.52 s

(B) for capacitor, Vma = EMF = 120 V

and Q = C V

Qmax = 1.80 x 10^-6 x 120 = 216 x 10^-6 C Or 216 uC

(C) Q = Qmax [ 1 -e^(-t/RC)]

20 = 216 [ 1 - e^(-t/ 2.52)]

e^(-t/2.52) = 0.907

t = - ln(0.907) x 2.52 = 0.245 sec

(D) Imax= E/R = 120 / (1.40 x 10^6) = 8.57 x 10^-5 A

(E) V = 120[ 1- e^(-t/RC]

V = 120 [ 1- e^(-0.1/2.52)] = 4.67 Volt

(g) now time constant = R C = 520 x 10^3 x 1.80 x 10^-6 = 0.936 sec

(h) V = 120 [ e^(-t/RC)]

V =120 e^(-0.400/ 0.936) = 78.27 Volt

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