How Did They Calculate Vo in the Circled Step?

[sammyqw]

Homework Statement

http://imgur.com/ZKiCbbA http://imgur.com/a/ccGTV

Could someone explain me what happened in the step that is circled in red please? I would appreciate it.
did they multiply i0x(iL)?

Homework Equations

they got iL by using iL=iL(initial)*e^-t/Tau . How did they get Vo? what formula did they use?

The Attempt at a Solution

http://imgur.com/a/wr1mQ[/B]

http://imgur.com/q4y6NXZ
http://imgur.com/a/wr1mQ

 

[sammyqw]

I think I got it. I did Current divider io= 40/40+10 (8e^-250t) . I got 6.4e^-250t Amps then using Ohms law with the 10ohm resistor I got 64e^-250t V can someone confirm it please?

 

[sammyqw]

and that 10ohm resistor in the far left should have the same voltage as the 40ohm resistor correct?

 

[gneill]

Your images are not visible. This will limit the responses from helpers who are browsing questions and can't be bothered to follow off-site links. It's a better practice to UPLOAD images so helpers don't have to follow links to see them.

I'll see if I can place copies of your images into your posts...

edit: ...done.

 

[sammyqw]

for some reason it wouldn't let me upload pictures from imgur. it works with postimg though :D I will use that method from now on.

 

[gneill]

and that 10ohm resistor in the far left should have the same voltage as the 40ohm resistor correct?

No, the inductor will have some potential difference across it as it attempts to drive current trough the circuit. So that PD plus the PD across the 10 Ω resistor will be the same as that across the 40 Ω resistor.

You'd be better off simplifying the circuit a bit before proceeding. When the switch commutates to position 2 it places the 4 Ω + 6 Ω series resistors in parallel with the 40 Ω resistor. So you're left with:

So, do with that what you will!

 

[sammyqw]

No, the inductor will have some potential difference across it as it attempts to drive current trough the circuit. So that PD plus the PD across the 10 Ω resistor will be the same as that across the 40 Ω resistor.

You'd be better off simplifying the circuit a bit before proceeding. When the switch commutates to position 2 it places the 4 Ω + 6 Ω series resistors in parallel with the 40 Ω resistor. So you're left with:
View attachment 107206

So, do with that what you will!

I was referring to these two circled resistors, don't they have the same voltage because they are in parallel? I found the io using current divider io=(40/50)(8e^-250t), then use that io to find vo with ohms law.

 

[gneill]

Yes they share the same potential difference. So your expression for the current through the 10 Ω resistance looks good.

 

[NascentOxygen]

I was referring to these two circled resistors, don't they have the same voltage because they are in parallel? I found the io using current divider io=(40/50)(8e^-250t), then use that io to find vo with ohms law.

You can do the current divider, then use one resistor and its current,
OR
you can use their total current and their combined resistance. Either way should give the same result.