Solve Kirchhoff Problem: Find I1, I2, I3

[James.Garland]

Homework Statement

Find I1, I2, I3
http://i58.tinypic.com/hwg4y0.png

(Problem included in image)

Homework Equations

Junction Rule, Kirchhoff, Ohms Law

The Attempt at a Solution

I don't understand Kirchhoff at all. All i got was I2=I1+I3 and I think that might be wrong.

 

[NascentOxygen]

Hi James.Garland! http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif

First thing: mark on each battery its positive end. You need that right, to start.

Next, what have you learned in class about starting to solve problems like this? How do you begin?

 

[James.Garland]

So the positive end on the 12 V is the left and the 9 V is the right.

We haven't really done these in class at all...

 

[James.Garland]

What do I do to start?

 

[epenguin]

We haven't really done these in class at all...

Working out for self, even part, even fail, will help you get most out of class afterwards.

Using Kirchhoff's current law, maybe this is being called junction rule, can you get a relation purely between I₁, I₂ and I₃?

After which you can maybe use KVL and Ohm's Law and combine to set up some equations you could solve.

 

[James.Garland]

Okay, so at the bottom junction it looks like I1 and I3 are going in and I2 is leaving, so is the junction rule

I1+I3=I2 ?

 

[NascentOxygen]

It's handy to have a zero volt reference, so declare the junction of the 3 resistors to be zero volts. All other voltages can be measured relative to that.

You could label the junction at the top of the 20 ohms to be V volts. Now determine an expression for each current in terms of that single unknown, V.

 

[James.Garland]

I don't really understand but are you saying to have

V=20*I2 - 15*I1 - 30*I3 ?

 

[epenguin]

Okay, so at the bottom junction it looks like I1 and I3 are going in and I2 is leaving, so is the junction rule

I1+I3=I2 ?

Yes

....

 

[NascentOxygen]

I don't really understand but are you saying to have

V=20*I2 - 15*I1 - 30*I3 ?

No. One at a time, find an expression for the current in each resistor, write it in terms of that V.

 

[James.Garland]

So for the next step, I think it is to write equations for the relationship between the individual loops, right?

So for the right loop, would it be

15 I1 +20 I2 = 9 Volts ?

and for the left,

20 I2 + 30 I3 = 12 Volts ?

 

[NascentOxygen]

So for the next step, I think it is to write equations for the relationship between the individual loops, right?

So for the right loop, would it be

15 I1 +20 I2 = 9 Volts ?

and for the left,

20 I2 + 30 I3 = 12 Volts ?

Yes. That's a good start. You don't need to label the V volts point I suggested, if you follow through with how you've begun.

What comes next?

 

[James.Garland]

I think next would be to use algebra and the three equations to solve for each, right? So,

I1 = .155
I2 = .332
I3 = .177

and this is amps, correct? Since it's current?

 

[NascentOxygen]

The units would be amps, yes. You can check that those values satisfy the equations you have, if no one else has worked out their answer for comparison.