# RC Multiloop Circuits, Find Current at Specific Time

1. Mar 20, 2017

### D Nguyen

1. The problem statement, all variables and given/known data

2. Relevant equations

For a basic RC circuit during charging:

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

3. 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.

2. Mar 20, 2017

### Staff: Mentor

Hi D Nguyen,

Welcome to Physics Forums!

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

3. Mar 20, 2017

### D Nguyen

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?

4. Mar 20, 2017

### Staff: Mentor

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?
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.

5. Mar 20, 2017

### D Nguyen

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!

6. Mar 20, 2017

### Staff: Mentor

7. Mar 20, 2017

### D Nguyen

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?

8. Mar 20, 2017

### Staff: Mentor

You could, but will anything change over time? One assumes that the circuit has already reached steady state before t = 0.

9. Mar 20, 2017

### D Nguyen

I don't think the circuit starts at steady state because the capacitor is initially uncharged.

10. Mar 20, 2017

### Staff: Mentor

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.