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Question

A resister with resistance 10 MΩ is connected in series with a capacitor of capacitance 1.0 muF and a battery with emf 12.0 V. 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 plates at time t=46s?
c. What fraction of the initial current remains at t=46 s?
1017945_55e7205f80d643f98ce5ea4868b083de.png

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Solution

a. The time constant is t=RC =10 X 106 X 1 X 106=10 s
b. The fraction f of the final charge on capacitor is qQ
qQ =1-etRC =1-e4610=0.99
The capacitor is 99% charged after a time kequal to 4.6 RC , or 4.6 timek constants.
c. II0 = e4.6 =0.010
After 4.6 timek constants, the current has decreased to 1.0 od ira initial value.

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