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RL circuit

  • Thread starter reising1
  • Start date
  • #1
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Homework Statement



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?

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!

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
LeonhardEuler
Gold Member
859
1
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:
reising1 said:
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?
 
  • #3
54
0
Oh, wait. That is wrong.

With respect to I, you get:

R + LI = 0

So I = -R/L?
 
  • #4
54
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Deriving with respect to I. Sorry.
 
  • #5
LeonhardEuler
Gold Member
859
1
This is still not right because you differentiated one term and integrated the other.
 
  • #6
LeonhardEuler
Gold Member
859
1
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?
 
  • #7
54
0
What do you mean?

d/di(RI) = R
d/di(L(di/dt)) = LI
 
  • #8
54
0
differential equation
 
  • #9
LeonhardEuler
Gold Member
859
1
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.
 
  • #10
LeonhardEuler
Gold Member
859
1

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