You have a basic \"R-C\" circuit without an EMF, such as the one shown above. Le

Question

You have a basic "R-C" circuit without an EMF, such as the one shown above. Let R = 8.00 kiloOhms, and C = 250 nanoFarads, and the capacitor is initially charged to a potential of 10.0 Volts. At time t = 0, the switch is closed and the capacitor begins to discharge.

a. What is the initial chrage on the capacitor, Q(0)?

b. What is the initial current that flows in the circuit immediately after the switch is closed?

c. At what time does the chrage on the capacitor diminish to 5.00% of its initital value?

Please show and explain your work.

Explanation / Answer

time constant of the circuit T = RC = 8000 *250*10^-9 = 2ms

a. initial charge Q0 = CV =0

b. initial current i = V/R = 10/8000 = 1.25 mA

c. Q= Q0(1-e^-t/T)

1-e^-t/T = 0.05

e^-t/T = 1-0.05 = 0.95

-t/T = ln(0.95) = -0.05

t = 0.05 * 2ms = 0.102 ms

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