Transient Response RC series circuit

[Physicist3]

Hi, I have been given a question which involves analysis of a series RC circuit. The system in question has a 4Ω resistor in series with a 1000μF Capacitor (the capacitor is to be considered as completely uncharged before t=0). There is a 12V supply in the circuit. At t=0, a switch is closed to complete the circuit. I have been asked to calculate the following and was wondering if someone could confirm whether or not my answers are correct;

i. - initial (t=0) current in the circuit.
ii.- initial voltage across the capacitor
iii- final voltage in the capacitor
iv- time constant of the circuit
v - current in the circuit at 6ms
vi - final energy stored in the capacitor

Answers

i. initial (t=0) current in circuit = V/R = 12/4 = 3.0A

ii. Initial voltage across the capacitor = 0V (as Capacitor is uncharged before switch is closed at t=0)

iii. final voltage in capacitor = V = 12V.

iv time constant of the circuit = ζ = CR = 1000 x 10^-6 * 4 = 4mS or 0.004S

v. current in circuit at t=6ms = i(t) = I_oe^(-t/ζ)
this = 3.0e^{-(0.006/0.004)} = 0.67A

vi - final energy stored in capacitor = E = (CV²/2) = (1000x10^-6 * 12²)/2 = 0.072J

Any feedback would be greatly appreciated! :)

 

[Jony130]

Your answer looks good. Only kept in mind that capital "S" is reserved for Siemens, electric conductance 1/Ω. For "time" use small "s".