How Do Current and Voltage Divide in Different Branches of a Circuit?

[Ithryndil]

Homework Statement

Determine the current in each branch of the circuit where R = 14.00 Ω, and V = 20.0 V.

(a) branch containing resistor R

(b) branch containing the 4.00 V source

(c) branch containing the voltage source V

Homework Equations

N/A

I have already completed the problem, but I want a bit of an explanation why things are they way they are in regards to the equations below:

I1+I2+I3 = 0
V1 - 6I1 - 14I3 = 0 (Left loop)
6I1 - 4I2 - V1 + V2 (Right loop)

Thanks for your help. I understand the one about the left loop, it's the right loop equation I am a bit hung up on.

 

[tiny-tim]

6I1 - 4I2 - V1 + V2 (Right loop)
…
it's the right loop equation I am a bit hung up on.

Hi Ithryndil!

I assume it's the + or - sign for the Is that are worrying you?

The way you draw the arrows for the three currents is entirely arbitrary.

Of course, it's nice to make an intelligent guess as to which way the current will flow, so that all the Is come out positive.

But it doesn't matter in the slightest if you guess wrong, and put one of the arrows the wrong way round …

suppose you had labelled the arrow on I2 the other way …

you'd then get 6I1 + 4I2 - V1 + V2 (and of course I1 = I2 + I3 instead of I1 + I2 = I3), and your I2 would come out negative.

Does that help?

 

[Ithryndil]

Yeah, I believe so. It's getting the signs the summation of it that had me, but after some further thought, I think I have it. I should probably redo the problem differently and see what I get.