Need help on college question!

Hi there and welcome to Electronics Point

We don't give answers to homework questions - that defeats the purpose of having homework in the first place! But we will try to push you in the right direction so you can solve it yourself.

The first thing to do is to redraw that circuit in its simplest form. Two tricks have been used to make it look more complicated than it is: R1 and R3 have been drawn in series with V1 but in different legs, and R4 and R5 have been drawn in series. In both cases these can be reduced to a single resistance.

When you do that, you will have a circuit with three resistors and two voltage sources. Each of the voltage sources will have one resistor in series with it. Start by drawing that circuit and labelling the resistors with their original circuit references and their total resistance values.

 

OK. So draw up the simplified circuit and post it, then we can analyse it using Kirchhoff's Law.

 

You've simplified it wrong. You've got the three resistor values right, but they aren't connected the right way.

It might help if you label each resistor with its original circuit reference. Since you will be combining R1 and R3, and combining R4 and R5, the three resistors in your simplified diagram will be named "R1+R3", "R2", and "R4+R5".