SPST switch RLC circuit help

[asdf12312]

Homework Statement

SPST switch closes at t=0. Find vC(0-) and iL(0-), iC(0) and vL(0), and vC(infinity) and iL(infinity).

Homework Equations

The Attempt at a Solution

kind of basic circuit, i know, but i just wanted to check my answers in case i did something wrong.

At t=0- : capacitor acts like open circuit, inductor like short circuit. also there no closed loops, so there's no current. vC(0-)=V(s)=12V, and iL(0-)=0.

at t=0: capaciator behaves like voltage source, inductor like current source of 0A. so would iC(0) be -3A? and vL(0)=12V.

at t=infinity: capacitor acts like open circuit, inductor like short circuit. vC(infinity)=0V, and iL(infinity)=4A.

 

[haxor489]

Looks right to me

 

[asdf12312]

anyone else?? did i do this right?

 

[rude man]

anyone else?? did i do this right?

Yes you did.

 

[rezeew]

Your analysis is mostly correct. At t=0, the capacitor will have an initial voltage of 12V, but since it acts like a voltage source, the current through it will depend on the rest of the circuit. In this case, since there is no closed loop, the current through the capacitor will be 0A. Therefore, iC(0) will also be 0A.

At t=infinity, the capacitor will have fully charged to 0V, so vC(infinity) will be 0V. The inductor will also behave like a short circuit, so the current through it will be determined by the voltage source of 12V and the resistance in the circuit. Since the resistance is 3 ohms, the current through the inductor will be 4A, as you correctly stated.

Overall, your analysis is correct, but just be careful with the signs of the currents at t=0. It's always a good idea to double check your calculations to make sure they make sense.