How can Kirchoff's rules be used to determine current values in a circuit?

[Azndude51]

Homework Statement

Use Kirchoff's rules to determine I1, I2 and I3 for the following circuit: https://chip.physics.purdue.edu/protected/Prelab221img/e4pp2.jpg

E1 = emf = 9 V
r = internal resistance = 1.5 ohms
R1 = 5 ohms
R2 = 15 ohms
R3 = 22.75 ohms

Find I1, I2, I3

Homework Equations

V=IR
I(R1+R2) = V and Req = R1 + R2+ ... for resistors in series
I = emf/R1 + emf/R2 + ... and 1/Req = 1/R1 + 1/R2 + ... for resistors in parallel
Krichoff's junction rule Iin-Iout = 0

The Attempt at a Solution

I found I1 to be .741 A by using I=V/R with R being the calculated total resistance: (1.5 + 1/(1/22.75+ 1/20) = 12.14

Now I've been using various combinations of the equations above to get the other two I's but I can't seem to get a correct answer, can someone point me in the right direction?

Thanks in advance

 

[ranger]

I found I1 to be .741 A by using I=V/R with R being the calculated total resistance: (1.5 + 1/(1/22.75+ 1/20) = 12.14

Correct

Now I've been using various combinations of the equations above to get the other two I's but I can't seem to get a correct answer, can someone point me in the right direction?

What exactly were you doing?
Note that I₁ = I₂ + I₃

 

[Azndude51]

So if I1 = I2 + I3, shouldn't I2 = I1 - I3 = .741 - 9/22.75 = .345?

 

[ranger]

Yup, that's correct.

 

[Azndude51]

DARN IT, I got .345 for I2 when I first tried the problem, but when I submitted it (online) it was wrong, so I posted here. But when I submit it for I3, it is correct (and .396 is correct when I submit that for I2). I think they must've gotten switched. Thanks for the help though, ranger.

 

[ranger]

I see what you mean. When I double checked them with the current divider rule, I noticed the same thing. Its just a small mix up, that's all.