(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find I_1, I_2 and I_3 if the switch, k, is closed using Kirchhoff's Rules.

2. Relevant equations

V=IR

3. The attempt at a solution

I've had multiple attempts at this and this one is the one that came closest to a solution.

Setting up 3 equations:

1) I_1 = 1_2 + I_3 => I_1 - I_2 - I_3 =0

2) 12V + I_3*(4 Ohm) - I_1*(7 Ohm) = 0

3) 12V - 9V - I_2*(5 Ohm) - I_1*(7 Ohm) = 0

2) 12 = 7*I_1 - 4*I_3 => 12 = 7*(I_2 + I_3) - 4*I_3 => 12 = 7*I_2 + 3*I_3

3) 3 = 7*I_1 + 5*I_2 => 3 = 7*(I_2 + I_3) + 5*I_2 => 3 = 12*I_2 + 7*I_3

Getting rid of I_3:

84 = 49*I_2 + 21*I_3

09 = 36*I_2 + 21*I_3

---------------------------

75 = 13*I_2

I_2 = 5.75

By substituting in, I get

I_1 = -3.7

I_3 = -9.5

Is this anywhere near correct, I don't know why, but somehow this seems fishy to me :S

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# Homework Help: Calculating current in circuit with multiple emf's using Kirchhoff's

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