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circuit shown in Figure 28.5 is constructed using a 6V battery, a 3k ohm resisto

ID: 1427936 • Letter: C

Question

circuit shown in Figure 28.5 is constructed using a 6V battery, a 3k ohm resistor, and a 6k ohm resistor. Initially both switches are open and the capacitor is uncharged. Switch A is closed and the capacitor begins to charge. After 1/2 second the potential difference across the capacitor is 3.78 V. What is the capacitance of the capacitor? After several minutes switch A is opened. What is the approximate potential difference across the capacitor? Switch B is now closed and the capacitor begins to discharge. What is the characteristic time for discharging this capacitor? will the current through the 6 k ohm resistor be after 2 seconds? What will the charge on the capacitor be after 3 seconds?

Explanation / Answer

a) at time t

v = vmax*(1 - e^(-t/T))

3.78 = 6*(1 - e^(-t/T))

3.78/6 = 1 - e^(-t/T)

e^(-t/T) = 1 - 3.78/6

-t/T = ln(0.37)


T = -t/ln(0.37)

R*C = -0.5/ln(0.37)

C = 0.503/R

= 0.503/(3*10^3)

= 1.68*10^-4 F

b) VC = Vmax = 6 volts

c) Time constant of the ckt, T = R*C

= 6*10^3*1.68*10^-4

= 1.008 s

d) I = Imax*e^(-t/T)

= (Vmax/R)*e^(-2/1)

= (6/(6*10^3))*e^(-2)

= 1.35*10^-4 A

e) Q = Qmax*e^(-t/T)

= (C*Vmax)*e^(-3/1)

= (1.68*10^-4*6)*e^(-3)

= 5.02*10^-5 C