## RL circuit

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

There is a Battery connected to a single loop circuit containing two resistors, R1 and R2, and one capacitor L.

After a long time, the battery is removed, so there is a single loop circuit with just two resistors and a capacitor.

What is the current going through R1?

3. The attempt at a solution

This is what I thought:

So, the EMF is removed. Thus, using a loop rule, we have the formula:

0 = IR + L(di/dt) where R is R1+R2

Integrating, we have

0 = (1/2)(I^2)(R) + (L)(I)

Dividing everything by I, we have

0 = (1/2)(I)(R) + L

Thus, I = (2L) / R

However, this is incorrect.

Any ideas?

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

2. Relevant equations

3. The attempt at a solution

Recognitions:
Gold Member
There are a few problems here. You call this an RL circuit, and you use the equations for an RL circuit, but you say it contains a capacitor instead of an inductor. I assume you are just using the wrong word.

The second problem is here:
 Quote by reising1 0 = IR + L(di/dt) where R is R1+R2 Integrating, we have 0 = (1/2)(I^2)(R) + (L)(I)
Are you sure you did that correctly? What variable are you integrating with respect to?
 Oh, wait. That is wrong. With respect to I, you get: R + LI = 0 So I = -R/L?

## RL circuit

Deriving with respect to I. Sorry.
 Recognitions: Gold Member This is still not right because you differentiated one term and integrated the other.
 Recognitions: Gold Member You might want to rethink the whole strategy of trying to take an integral or a derivative. You have both I and dI/dt in this equation. What kind of equation does that make it?
 What do you mean? d/di(RI) = R d/di(L(di/dt)) = LI
 differential equation

Recognitions:
Gold Member
 Quote by reising1 What do you mean? d/di(RI) = R d/di(L(di/dt)) = LI
Taking a derivative of a derivative doesn't make the derivative do away.

Recognitions:
Gold Member
 Quote by reising1 differential equation
Yes!

 Tags capacitance, current, resistor, rl circuit, series