• Support PF! Buy your school textbooks, materials and every day products Here!

L-C-R Circuit - finding current

  • Thread starter ttiger2k7
  • Start date
  • #1
58
0
[SOLVED] L-C-R Circuit - finding current

1. Homework Statement
In the figure below, V = 100.0 V, R1 = 40.0 Ohms, R2= R3 = 36.0 Ohms , and L = 17.0 H. No current flows until switch S is closed at t=0. Find the magnitude of the current i1 immediately after the switch is closed.

http://calculus.unl.edu/edu/classes/JF05/LRC.gif [Broken]


2. Homework Equations
Kirchoff's loop rule

Voltage across Inductor: [tex]L\frac{di}{dt}[/tex]


3. The Attempt at a Solution

Since [tex]R_{2}[/tex] and [tex]R_{3}[/tex] are in series I can add them:

36 Ohms + 36 Ohms = 72 Ohms

And applying the loop rule:

[tex]V - iR_{1} - L\frac{di}{dt} - iR_{2+3} = 0[/tex]
[tex]100 V - i(40 Ohms) - ???? - i(72 Ohms) = 0[/tex]

---

I have two questions regarding this problem:

Is applying the Loop rule the right way to go?

And if so, what exactly is [tex]L\frac{di}{dt}[/tex]? Isn't it just [tex]\frac{\epsilon}{L}[/tex]?
 
Last edited by a moderator:

Answers and Replies

  • #2
536
2
It's much easier than you thought. "Immediately after the switch is closed" is the easiest kind of question to answer. It takes time for the current through an inductor to build up. (Or, if this were a capacitor problem instead of an inductor problem, I would be saying: it takes time for the voltage across a capacitor to build up).

So right after the switch is closed, with i3 beginning at zero, the inductor is like an "open switch".

But remember that this is true only for a point in time -- then i3 will increase asymptotically toward some final value.
 
  • #3
58
0
thank you!
 

Related Threads for: L-C-R Circuit - finding current

Replies
5
Views
2K
  • Last Post
Replies
10
Views
3K
  • Last Post
Replies
5
Views
6K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
1
Views
7K
Replies
3
Views
2K
Replies
5
Views
1K
  • Last Post
Replies
2
Views
2K
Top