RL circuit


by reising1
Tags: capacitance, current, resistor, rl circuit, series
reising1
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#1
Apr3-10, 04:22 PM
P: 55
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
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LeonhardEuler
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#2
Apr3-10, 05:20 PM
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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 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?
reising1
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#3
Apr3-10, 05:34 PM
P: 55
Oh, wait. That is wrong.

With respect to I, you get:

R + LI = 0

So I = -R/L?

reising1
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#4
Apr3-10, 05:34 PM
P: 55

RL circuit


Deriving with respect to I. Sorry.
LeonhardEuler
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#5
Apr3-10, 05:36 PM
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This is still not right because you differentiated one term and integrated the other.
LeonhardEuler
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#6
Apr3-10, 05:38 PM
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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?
reising1
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#7
Apr3-10, 05:38 PM
P: 55
What do you mean?

d/di(RI) = R
d/di(L(di/dt)) = LI
reising1
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#8
Apr3-10, 05:38 PM
P: 55
differential equation
LeonhardEuler
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#9
Apr3-10, 05:39 PM
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Quote Quote by reising1 View Post
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.
LeonhardEuler
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#10
Apr3-10, 05:39 PM
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Quote Quote by reising1 View Post
differential equation
Yes!


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