A 20 kn resistor and a 3 capacitor are connected in series to a 3 V battery. At

Question

A 20 kn resistor and a 3 capacitor are connected in series to a 3 V battery. At t-0, the circuit is connected, and the capacitor has no charge on its plates. (a) What is the time constant of the cirouit? (b) AL t 0.12 s, what is the magnitude of the charge on each plate? 9- 12e-6 x c (c) In the limit as t approaches oo, Q approaches a maximum value. What is Qmaa? (d) What is the voltage across the capacitor at t 0? (e) What is the voltage across the capacitor at t 12 s? What is the voltage across the capacitor at t-co? (g) What is the current through the resistor at t-0 s? What is the current through the resistor at t-0.12 s? What is the current through the resistor att

Explanation / Answer

b] Q = CV[1 - e-t/RC]

=> Q = 7.782 x 10-6 C

e] V = 3[1 - e-t/RC]

=> V = 2.594 volts

f] at t = infinity, voltage across capacitor = EMF = 3volts.

g] At t = 0s, Io = 3/20,000 = 150 uA.

h] I = Ioe-t/RC

=> I = 20.3uA.

f] I = 0 A.

voltage across resistor = emf - voltage across capacitor.

Voltage across capacitor is been evaluated above. Take the difference to get the voltage across resistor.

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