R-L Circuit, Finding the current through a circuit element.

1. Mar 31, 2013

hyddro

1. The problem statement, all variables and given/known data
So I am having a hard time trying figuring this out. The question asks for the current through the 20Ω resistor as well as the current through the battery AFTER THE SWITCH HAS BEEN CLOSE FOR ALONG TIME.

Here is a picture of the circuit.

http://i.imgur.com/VjoFSUd.jpg

2. Relevant equations

Kirchhoff Loop rule.
Kirchhoff node rule.

V_L = L*di/dt

V=iR.

i = I (e^(-t(R/L)))

3. The attempt at a solution

Here is how I tried figuring it out. After a long time di/dt =0 so the potential across the inductor is 0. If that is the case then by Kirchhoff Loop rule (outer loop) E - 10Ω*I - V_L = 0 or 30 - 10Ω*I - V_L = 0
since V_L = 0, then the current through the resistor (and the battery) would be 3A. Now, when I appply the loop rule on the right loop. V_L - 20Ω(I) = 0. Again, Since V_L = 0 then the current through the 20Ω resistor must be zero, but this doesn't make any sense to me, i just don't know why but I feel this is wrong. Can anyone confirm this? Also, if this is right, why is the current through that resistor 0 ? Thank you

2. Mar 31, 2013

rude man

You just figured out that the voltage across the inductor is zero, and the 20 ohm is across the inductor also. So what would be the voltage across the 20 ohm resistor? the current?

3. Mar 31, 2013

hyddro

Oh Yeah! They are connected in parallel, so the Potential across the inductor must be equal to the potential across the 20 ohm resistor, if that is the case then the potential across the resistor is 0, from Ohm's law, 0=I.R, so I must be zero as well... Is this correct? Why is the current 0? I mean mathematically this makes sense, but in terms of the role of an inductor in a circut, why is this happening? What happens if we replace this inductor with a piece of wire and close the switch? would this scenario still happen? Thank you!

4. Mar 31, 2013

rude man

Well, why shouldn't the current thru the 20 ohm be zero?

If you let current in an iinductor settle at a constant value - any constant vaue including zero - then the voltage across that inductor is zero.

If you replaced the inductor with a wire then obviously the current thru the 20 ohm would always be zero.

Ashort wire is an inductor with a very low inductance (a few nanohenries typically).

5. Mar 31, 2013

hyddro

ok that was really helpful. Thank you Rude man! hehe

6. Apr 1, 2013

Edit....