RLC Circuits (Second-Order Circuits)

[Pis]

I using LTSPice and PSpice to do a simulation eith RLC circuits. This is my first time using LTSpice for rlc simulation. The problem is, I don't know to handle RLC circuits using LTSpice. PSpice, i haven't try yet.


This is the circuit.


This is my drawing using LTSPice

I already run the simulation, but, I think, my setting is wrong, for RLC circuits, is different, i cannot directly just input the dc value right?....i confused, please help me...anyone...

1) I want to find V(t) and Vr(t) for t>0 for R=10, R=20, and R=30 Ohm...so i want to verify my answer with this simulation using LTspice...

2) Then i want determine v(t) for t=0.8s...

Thank you, this is my first time, using ltspice for rlc circuits...

[Fu-Kwun Hwang]

Your problem can be solved analytically.
The switch between capacitor and 2Ω opened at t=0, it means that the capacitor is charged to 12V*2/3=8V at t=0.
The problem reduced to RLC circuit with initial conditions:
t=0;
 I=0, Vc=8V, V_R=0V, V_L=2V (V_L=10-Vc-V_R )
The differential equation need to be solved is $10=L \frac{dI}{dt}+IR+\frac{1}{C}\int I dt$
or $L\frac{d^Q}{dt^2}+I\frac{dQ}{dt}+\frac{Q}{c}=0$

The solution is similar to a spring with constant k, attached with mass m and damping constant b.
$m\frac{d^2x}{dt^2}+b\frac{dx}{dt}+kx=0$

The analytical solution can be found in standard textbook.

You are also welcomed to check out RLC circuit simulation (DC Voltage source) to find out the simulated solution.

[Pis]

Your problem can be solved analytically.
The switch between capacitor and 2Ω opened at t=0, it means that the capacitor is charged to 12V*2/3=8V at t=0.
The problem reduced to RLC circuit with initial conditions:
t=0;
 I=0, Vc=8V, V_R=0V, V_L=2V (V_L=10-Vc-V_R )
The differential equation need to be solved is $10=L \frac{dI}{dt}+IR+\frac{1}{C}\int I dt$
or $L\frac{d^Q}{dt^2}+I\frac{dQ}{dt}+\frac{Q}{c}=0$

The solution is similar to a spring with constant k, attached with mass m and damping constant b.
$m\frac{d^2x}{dt^2}+b\frac{dx}{dt}+kx=0$

The analytical solution can be found in standard textbook.

You are also welcomed to check out RLC circuit simulation (DC Voltage source) to find out the simulated solution.

Oh, ok, thanks, this problem already solved.

I must put in the initial condition for capacitor, 8V.

So my circuit will become like this:


I simplified it. IC=Initial condition.

Then, settings:


Tick "Skip initial operating..."

Finally, become like this:



Then I just run the simulation for the graph. Must put the equation also for V(t) and Vr(t)...

Already solved, thanks! 

[Fu-Kwun Hwang]

It is great that you can solve it by yourself!