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**1. Homework Statement**

The 5.00-V battery in the figure ( http://session.masteringphysics.com/problemAsset/1009413/11/yf_Figure_26_42.jpg ) is removed from the circuit and replaced by a 20.00-V battery, with its negative terminal next to point b. The rest of the circuit is as shown in the figure.

a) Find the magnitude of current in the upper branch.

b) Find the magnitude of current in the middle branch.

c) Find the magnitude of current in the lower branch.

d) Find the potential difference Vab of point a relative to point b.

**2. Homework Equations**

Kirkoff's loop law: V1 + V2 + V3 = 0

Kirkoff's junction law: Current in = Current out

**3. The Attempt at a Solution**

For the top branch, I made current equal to I

_{1}, second branch I

_{2}, third branch (I

_{1}+I

_{2}).

It's sort of hard to explain how I tried to do it, but here it goes:

First I looked at the top 2 branches, going clockwise, starting with the first resistor at the left on the top branch.

2(I

_{1}) - 10V + 3(I

_{1}) - 4(I

_{2}) + 20 - I

_{2}= 0

Since there are two variables, I did the same thing for the middle and bottom branch.

Starting on the middle branch, the resistor on the right...

4(I

_{2}) - 10(I

_{1}+ I

_{2}) + I

_{2}- 20V = 0

Isolating I

_{2}from the second part I got I

_{2}= -4 - 2I

_{1}.

I substituted this into the first equation, but did not get the right answer.

Not sure how to even start with finding the potential difference.

Any explanation would be greatly appreciated!!