A resistor with resistance 14 M ? is connected in series with a capacitor with c

Question

A resistor with resistance 14 M? is connected in series with a capacitor with capacitance 1.0?F and a battery with emf 13.5V. Before the switch is closed at time t=0, the capacitor is uncharged.

(a) What is the time constant?

(b) What fraction of the final charge is on the plastes at time t=47s?

(c) What fraction of the initial current remains at t=47s?

(d) If the capacitor is orginally given a charge of 7.0 ?C and then is discharged by closing the switch at t=0, at what time will the charge be equal to 0.550 ?C? and What is the current at this time?

Explanation / Answer

1)tau=RC=14E6*1E-6=14s
2)Q=Qm( 1-e^(-t/tau)
Q/Qm = 1 - e^(-47/14)=0.9652
3) I/IZ = e^(-t/tau)= e^(-47/14)=0.034
4) Q = Q0 e^(-t/tau)
0.55 = 7 e^(-t/14)
t=35s
7E-6/14 e^(-35.6/14)=6.3E-6A

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