I'm working on a project wherein I need to calculate the maximum current that flows through a basic RLC circuit. I basically have a 1mH capacitor that I charge up to 100v, then discharge through a 100uH inductor with an internal resistance of 500 milliohms (these numbers are random values as I don't have access to the actual components at the moment to measure them). I've attached an image below to hopefully make my question clearer. I would think that calculating I_max in an RLC circuit would be rather elementary, but so far I have not found an equation for it. I have found equations for RL, RC, and LC circuits, but not for RLC. I also haven't been able to derive an equation that gives me a reasonable answer. This is for a school project, so i don't mind doing a bit of research if someone can point me in the right direction. However, finding this equation is not my main assignment, so giving me the actual equation would be great too.
Thanks!
~Josh Blackburn

 

When you first throw the switch, the peak current in the capacitor is very high because it tries to charge the capacitance to 100V instantaneously, which would require infinite current.

Since this is DC assuming C and L are ideal, the maximum current after an infinite amount of time is 100V/R. This is because eventually C tends toward infinite resistance and L tends toward zero resistance at DC.

 

Do you have TWO switches there? Is the one between the capacitor and the inductor initially open while the capacitor charges, then the switch between the power supply and the capacitor is opened prior to the other one being closed?

That's the only thing that makes sense give the traces you show.

Without running the numbers, I would have expended the circuit to ring (oscillate) given only 500 mΩ of resistance. But perhaps the damping factor is high enough to yield what you show.

Consider reading up the transient response of RLC circuits. This might be a good place to start.

https://en.wikipedia.org/wiki/RLC_circuit#Series_RLC_circuit

 

I’ll add that the equations governing the behavior of the 3 ideal components can be solved for current versus time. Perhaps you know how to find the maximum of an equation?

 

When you first throw the switch, the peak current in the capacitor is very high because it tries to charge the capacitance to 100V instantaneously, which would require infinite current.

Since this is DC assuming C and L are ideal, the maximum current after an infinite amount of time is 100V/R. This is because eventually C tends toward infinite resistance and L tends toward zero resistance at DC.

Sorry, I think the picture may have been confusing. The switch between the power supply and the capacitor is only to charge the capacitor to 100v. The real process I'm looking at is after the capacitor is charged to 100v, when the switch in the RLC circuit is closed. For this problem, you can ignore the power supply, just assume it's disconnected and that the capacitor starts with a full charge.

I’ll add that the equations governing the behavior of the 3 ideal components can be solved for current versus time. Perhaps you know how to find the maximum of an equation?

That would be helpful, thank you.

Do you have TWO switches there? Is the one between the capacitor and the inductor initially open while the capacitor charges, then the switch between the power supply and the capacitor is opened prior to the other one being closed?

That's the only thing that makes sense give the traces you show.

Without running the numbers, I would have expended the circuit to ring (oscillate) given only 500 mΩ of resistance. But perhaps the damping factor is high enough to yield what you show.

Consider reading up the transient response of RLC circuits. This might be a good place to start.

https://en.wikipedia.org/wiki/RLC_circuit#Series_RLC_circuit

Yes, that's exactly what is happening in the simulation, sorry if that wasn't clear. I've already read the wikipedia page you linked to, but thank you. I have a fairly decent understanding of RLC, RL, RC, LC circuits from several of my courses so far.

 

1mH capacitor is nonsense.

 

Yes, that's exactly what is happening in the simulation, sorry if that wasn't clear. I've already read the wikipedia page you linked to, but thank you. I have a fairly decent understanding of RLC, RL, RC, LC circuits from several of my courses so far.

Then what's the problem? Take the solution for i(t) in the inductor and solve it for the max value.

 

1mH capacitor is nonsense.

Ok it's pretty obvious that I meant 1mF.

 

Then what's the problem? Take the solution for i(t) in the inductor and solve it for the max value.

I could definitely do that, the issue is I have to find the maximum current through this circuit with a wide range of inductance values (i have a lot of inductors). I know there has to be an equation for max current that involves just the component values, not time.

 

You have two differential equations at play.

1) the discharge current of C, where i(t) = C dv/dt

2) the voltage across L, v(t) = L di/dt

 

I could definitely do that, the issue is I have to find the maximum current through this circuit with a wide range of inductance values (i have a lot of inductors). I know there has to be an equation for max current that involves just the component values, not time.

So solve the equation for the max current in terms of R, L, and C.