Circuit Analysis Problem #5 - Guidance Needed

[brad sue]

Homework Statement

Hi,
I have problem doing this problem:
It is the problem #5 on the attachment.( I was not able to remove problem#4)

Please can you give me some guidance?

Thank you
B

Homework Equations

The Attempt at a Solution

I know that for t>0( steady state) the inductor is like a short and the capacitor like an open circuit.

Do I need to replace the inductor by a short and cancel the part with the capacitor and then do a KVL and solve for V(t)?

I was wondering if I need to use the initial value (just before the switch closes).

Thank you
B.

 

[CEL]

Homework Statement

Hi,
I have problem doing this problem:
It is the problem #5 on the attachment.( I was not able to remove problem#4)

Please can you give me some guidance?

Thank you
B

Homework Equations

The Attempt at a Solution

I know that for t>0( steady state) the inductor is like a short and the capacitor like an open circuit.

Do I need to replace the inductor by a short and cancel the part with the capacitor and then do a KVL and solve for V(t)?

I was wondering if I need to use the initial value (just before the switch closes).

Thank you
B.

Steady state is not for t>0, is for t equal infinity. For 0 < t < infinity you have the transient. That is what the problem asks for.
For t > 0 you must use the properties of the inductor and the capacitor: $$v_L = L\frac{di_L}{dt}$$ and $$i_C = C\frac{dv_C}{dt}$$. Use Kirchoffs laws to form a second order differential equation, involving either $$i_L$$ or $$v_C$$.
Since you have a nonhomogeneous equation, the general solution is the sum of the solution of the homogeneos equation and one particular solution.
The particular solution can be obtained using the steady state, when the inductor is a short circuit and the capacitor an open circuit.
The general solution involves two integration constants. In order to obtain their values, you use the initial conditions.

 

[piercas]

Hi B,

Thank you for reaching out for guidance on this circuit analysis problem. Based on the information provided, it seems like you have a good understanding of the behavior of the inductor and capacitor in steady state. Yes, you are correct in thinking that you can replace the inductor with a short and the capacitor with an open circuit, and then use KVL to solve for V(t).

As for the initial value, it depends on the specific problem and what information is given. If the initial value is given, then it should be taken into consideration when solving for V(t). If the initial value is not given, then you can assume it to be zero or use a general expression for the initial value.

I hope this helps guide you in the right direction. If you need further assistance, please provide more specific information about the circuit and the problem. Good luck!