Applying Kirchhoff's Laws to Solve Circuit Problems

[Masterx00]

Homework Statement

Find I₁,I₂,I₃

Homework Equations

Attached the circuit diagram

2. The attempt at a solution

I₁ - I₂ + I₃ = 0

-120I₁ - 60I₂ + 0I₃ = -1.8

0I₁ -60I₂ -20I₃ = -1.2

I₁ = 1/150 A

I₂ = 1/60 A

I₃ = 1/100 A

Is that correct ? The answer is my textbook is different :(

 

[tiny-tim]

Welcome to PF!

Hi Masterx00! Welcome to PF!

I₁ - I₂ + I₃ = 0

Nooo …

 

[Masterx00]

Thanks :)
I took the 1st loop clockwise and the second loop anticlockwise, so why the 1st equation is wrong then ?
Can you please explain further ? :)

 

[tiny-tim]

Thanks :)
I took the 1st loop clockwise and the second loop anticlockwise, so why the 1st equation is wrong then ?
Can you please explain further ? :)

Your 1st equation (I₁ - I₂ + I₃ = 0) doesn't involve loops, it's for a vertex, so it only involves "in" or "out".

According to the diagram, I₁ is in, and both I₂ and I₃ are out.

 

[Masterx00]

Your 1st equation (I₁ - I₂ + I₃ = 0) doesn't involve loops, it's for a vertex, so it only involves "in" or "out".

According to the diagram, I₁ is in, and both I₂ and I₃ are out.

But, If I made it I₁ - I₂ - I₃ = 0, I1 = 0, I2 = 0.03, I3=-0.03, that sounds correct ?

 

[tiny-tim]

I1 = 0, I2 = 0.03, I3=-0.03, that sounds correct ?

No … how did you get that?

 

[tomeatworld]

Kirchhoff's first law says that the current into a juction is equal to the juntion out. So use that on the top middle junction and have another think about that first question (remembering the directions of currents!)

Could I also ask if the current directions were given or if you chose them?

 

[Masterx00]

No … how did you get that?

By substituting it with the other 2 equations (using the calculator eqn solver):
I1 - I2 - I3 = 0

-120I1 - 60I2 + 0I3 = -1.8

0I1 -60I2 -20I3 = -1.2

 

[tiny-tim]

0I1 -60I2 -20I3 = -1.2

No, I₂ and I₃ are in opposite directions.

 

[Masterx00]

aha
Now it gives correct answer (0.02,-0.01,0.03), I though direction of I3 was same like I1, because of the direction of the drawn battery poles :shy:
Thanks for help tiny-tim