# Transient Response RC series circuit

• Engineering
• Physicist3
In summary, the conversation is about calculating various values for a series RC circuit with a 4Ω resistor, 1000μF capacitor, and 12V supply. The initial current in the circuit is 3.0A, the initial voltage across the capacitor is 0V, the final voltage in the capacitor is 12V, the time constant of the circuit is 4mS or 0.004S, the current in the circuit at 6ms is 0.67A, and the final energy stored in the capacitor is 0.072J. Feedback on the answer is welcome.

#### 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

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) = Ioe(-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! :)

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