What are the currents at each resistor?

[chuvacjoe]

1. The problem statement, all variables

and given/known data

Homework Equations

I3 + I1= I2

The Attempt at a Solution

[/B]

 

[TSny]

Hello and welcome to PF!

It is very important to specify the directions that you are assuming for each of the three currents. Otherwise, there is no way for us to check the signs in your equations.

For each equation you should state whether it comes from a junction rule or from a loop rule; and, tell us which junction/loop corresponds to each equation.

 

[chuvacjoe]

Equation #1- Kirchoff's junction current rule
Equation #2- Upper Loop clockwise from 20V source
Equations #3- Lower Loop rule counterclockwise

 

[TSny]

Please specify the direction you are choosing for $I_1$, the direction you are choosing for $I_2$, and the direction you are choosing for $I_3$. This is essential for getting the correct signs in the equations.

 

[chuvacjoe]

That's probably where my mistake is at, but I3 counterclockwise, I 2 counterclockwise, and I 1 counterclockwise? This is the part I'm a little confused about because I've been learning kirchhoffs rules from a book and khan's academy. They all flow to the closest stronger volt source?

 

[TSny]

It would be clearer if you specified $I_1$ as to the right or to the left through the 30Ω resistor. Similarly for the other two currents. On your circuit diagram, these directions should be indicated with arrows.

 

[chuvacjoe]

I 1 to the right, I 3 to the right, and i 2 to the left as assumed from my first equation I 1 +I 3=i 2

 

[TSny]

I 1 to the right, I 3 to the right, and i 2 to the left as assumed from my first equation I 1 +I 3=i 2

Note that the equation I₁ + I₃ = I₂ would have also resulted from taking I₁ to the left, I₃ to the left and I₂ to the right.

But, OK. We now have definite directions for the currents: I₁ to the right, I₃ to the right, and I₂ to the left.

Your junction equation I₁ + I₃ = I₂ is correct.

Let's look at your loop equation for the top loop. You wrote

20 - 30I₁ + 5I₂ - 10 = 0.

There is a sign error in this equation. Can you explain why you chose each of the four signs on the left?
Why +20? Why - 30I₁? Why +5I₂? Why -10?

 

[TSny]

It is important to note that you generally will not know ahead of time the correct directions for the currents. That is part of what you will determine when solving the problem. But, the nice thing is that you can assume any direction you want for any of the currents. If your initial choice of direction for a current turns out to be wrong, then you will get a negative answer for that current. The negative sign indicates that the current is actually in the opposite direction from what you initially assumed.

So, for example, if you end up getting I₂ = -4 A, then the current I₂ will be 4 A in a direction opposite of what you initially chose when setting up your equations.

But it is essential to make an initial choice for the direction of each current and stick with that choice while setting up the signs in your equations.