# RC Multiloop Circuits, Find Current at Specific Time

## Homework Equations

For a basic RC circuit during charging:

q = CV(1-e-t/RC)
i = V/R (e-t/RC)

## The Attempt at a Solution

I can solve basic RC circuits but this is just out of my realm of understanding. I can also find the max charge of the capacitor. I'm not looking for a full solution yet, I'm just hoping for someone to tell me if the best strategy is to:

1. Set up a lot of equation with Kirchoff's rules and solve a differential equation,
2. Use the fact that the current through R3 will increase from some minimum to to maximum exponentially (though I wouldn't know what the time constant would be), or
3. Use another strategy.

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gneill
Mentor
Hi D Nguyen,

Welcome to Physics Forums!

Big Hint: Ask yourself if closing the switch will affect anything to the right of E2.

Hi D Nguyen,

Welcome to Physics Forums!

Big Hint: Ask yourself if closing the switch will affect anything to the right of E2.
Hello! Thanks for the welcome!

I think it will? E1 will push more current to the right of E2?

I tried another approach using Thevenin equivalent circuits. I got E(Thevenin) = 3.33 V and R(Thevenin) = 13.33 ohms. Then I would just use an RC circuit with those values of E and R?

gneill
Mentor
Hello! Thanks for the welcome!

I think it will? E1 will push more current to the right of E2?
What pushes current? What potential difference drives current in the right side of the circuit? Can the potential across E2 change when the switch is closed?
I tried another approach using Thevenin equivalent circuits. I got E(Thevenin) = 3.33 V and R(Thevenin) = 13.33 ohms. Then I would just use an RC circuit with those values of E and R?
A Thevenin approach is good when you need to find the equivalent resistance for an RC circuit. In this case you need to be a bit careful that you aren't looking at the t = -∞ case rather than the t = 0+ case.

Try this. Break the circuit here:

and find the Thevenin equivalent of the sources for both cases: switch open and switch closed.

What pushes current? What potential difference drives current in the right side of the circuit? Can the potential across E2 change when the switch is closed?

OK, I think it's starting to make sense. The potential across E2 can't change when the switch it closed, so open or closed, I can ignore E1 and R1? Then I use Thevenin?

A Thevenin approach is good when you need to find the equivalent resistance for an RC circuit. In this case you need to be a bit careful that you aren't looking at the t = -∞ case rather than the t = 0+ case.

Try this. Break the circuit here:
View attachment 114817

and find the Thevenin equivalent of the sources for both cases: switch open and switch closed.
Can I use a Thevenin approach for a question like this? I'm trying to use information from this website: https://www.allaboutcircuits.com/textbook/direct-current/chpt-16/complex-circuits/

Thanks for all of your help and patience!

What pushes current? What potential difference drives current in the right side of the circuit? Can the potential across E2 change when the switch is closed?
OK, I think it's starting to make sense. The potential across E2 can't change when the switch it closed, so open or closed, I can ignore E1 and R1? Then I use Thevenin?

gneill
Mentor
OK, I think it's starting to make sense. The potential across E2 can't change when the switch it closed, so open or closed, I can ignore E1 and R1? Then I use Thevenin?
You could, but will anything change over time? One assumes that the circuit has already reached steady state before t = 0.

You could, but will anything change over time? One assumes that the circuit has already reached steady state before t = 0.
I don't think the circuit starts at steady state because the capacitor is initially uncharged.

gneill
Mentor
I don't think the circuit starts at steady state because the capacitor is initially uncharged.
Okay, I hadn't considered that detail. I had assumed that the circuit was assembled for some time before t=0 when the switch was closed. But if you wish to treat E2 as "turning on" at t = 0, then by all means use Thevenin to reduce the supply to a single source and resistor.