Potential Difference in a Circuit

[mollybethe]

Homework Statement

What is the current and potential difference across the 4Ω, 12Ω, and 8Ω resistors.
What is the potential difference across a and b
https://fbcdn-sphotos-a.akamaihd.net/hphotos-ak-ash4/389632_3598331272733_1107039398_3285590_155442550_n.jpg

Homework Equations

V=IR
ΔV=ε-IR

The Attempt at a Solution

What we are having difficulty finding out is the potential difference across the resistors. What we are unsure of is whether the potential difference the change in Voltage as it goes through the resistor or the Voltage after it goes through the resistor. Our teacher gave us rather original way to solve this, so please don't knock it...too much.

we found I in the top loop is 1 amp and I in the bottom is 1.5 amps. We have also determined the potential difference from a to b (which isn't written on the image, but is from the junction on the right to the junction on the right). It seems really obvious, but we are just not sure which figure we are supposed to use to determine it and the solution in the book is just confusing us. Thanks!

 

[gneill]

You should make your symbols for the voltage sources more clear so that their polarity is obvious; add the + sign to the positive terminal.

Potential differences across a component is just that: the potential change as measured from one terminal of the component to the other. Usually when you're asked for this you can respond with the absolute value (a positive value), taking the potential change to be in the direction of current flow through the given component. If the problem specifies a particular direction to measure the potential change (even if it is against the current flow) then be sure to use follow that direction.

You should draw in your loop currents to determine the actual direction of the potential changes across the resistors. What value are you going to give to the current in the center branch?

Draw in your currents and mark the potential changes across the resistors. Ohms law will give you their values.