Finding current in a dual battery, triple resistor circuit.

[Gavandeshaq]

Homework Statement

Find the current in each branch of the circuit shown in the diagram (attached) if:
V₁ = 1V
V₂ = 4V
R₁ = 1$$\Omega$$
R₂ = 2$$\Omega$$
R₃ = 1$$\Omega$$

Homework Equations

V=I*R

The Attempt at a Solution

Okay, so I know that the voltage will be even across the parallel resistors and that the current can easily be worked from there. But I've never come across a circuit with 2 batteries in such awkward positions before. It just has me confounded...

 

[Redbelly98]

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[Gavandeshaq]

Sorry, I did do this before thinking I had attached it, but I must have done something wrong.
Here it is.

 

[Redbelly98]

This problem can be solved using Kirchhoff's voltage and current laws, so try that. (It can't be solved by finding parallel and/or series resistors, since none of them are in parallel or series.)

 

[Gavandeshaq]

Is this right? It seemed very simple to work out (although it is the first question on this worksheet).
I have a feeling I'm supposed to treat that central resistor as in parallel with both the right resistor and then the left resistor seperately.

 

[gneill]

You don't need quite so many currents; the current through components in series is the same for each component. So you really just need one current for each branch.

If you identify the three currents as in the attached diagram, label the voltage at the top node Va, and take the "common" reference point to be where the ground symbol is, then you should be able to write one voltage sum equation for each branch and one current sum for the node "a".

The current sum is I1 + I2 + I3 = 0.

The voltage sum for the first branch is: I1*R1 + V1 = Va

Can you write the other two equations?

 

[Gavandeshaq]

I3*R3 + V2 = Va
I2*R2 + V1 + V2 = Va

If that's correct, I assume I use simultaneous equations from here?

 

[gneill]

Your first equation is fine. I don't understand how you formed the second.

There are three branches that extend from the node labeled with Va down to the common node at the bottom. Your first equation embodies the situation for the rightmost branch. You need to write two more such equations, one each for the other two branches, then solve the three simultaneous equations for I1, I2, and I3.