Please show me how to get the correct answer which was 12.04 Thank you! A 2 kilo

Question

Please show me how to get the correct answer which was 12.04

Thank you!

A 2 kilo-ohm resistor and a 6 microfarad capacitor are initially connected in series to a 58 volt battery. After 24.6 milliseconds, the battery is removed from the circuit. What is the current in the circuit 8.9 milliseconds after the battery has been removed, in milliamps?

Please show me how to get the correct answer which was 12.04

Thank you!

A 2 kilo-ohm resistor and a 6 microfarad capacitor are initially connected in series to a 58 volt battery. After 24.6 milliseconds, the battery is removed from the circuit. What is the current in the circuit 8.9 milliseconds after the battery has been removed, in milliamps?

[None Given]

12.04 ± 10%

Explanation / Answer

resistance R=2000 ohms

capacitance C=6*10^-6 F

battery potenetial Vo=58 v

time constant, T=R*C=2000*6*10^-6

T=0.012 sec

here,

after t=24.6 msec

current, i=io*e^-t/T (here, io=Vo/R)

i=Vo/R*e^(-t/RC) ( charging process)

i=58/(2000)*e^(-24.6*10^-3/0.012)

i=3.73*10^-3 A

i=3.73 mA

now,

after removing of baatery

and after time t=8.9 msec (discharging process)

current, i'=i*e^-t/T (here, i=3.73 mA)

i'=3.73*10^-3*e^(-8.9*10^-3/0.012)

i'=1.78 mA

and

current in circuit after t=8.9 msec

i=vo/(R)*e^(-t/RC) - i'

=58/(2000)*e^(-8.9*10^-3/0.012) - 1.78*10^-3

=12.03 mA

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