Magnitude/Direction of Current in a Circuit

[vrobins1]

Homework Statement

Find the magnitude of the current in each branch of the circuit shown below, in which B1 = 1.83 V. Specify the direction of each current.

http://img183.imageshack.us/img183/6951/physics.gif

I labeled + and - and drew the assumed currents, with I₃ flowing to the right along the middle, I₁ flowing CW about the top loop, and I₂ flowing CCW about the bottom loop.

Homework Equations

The Loop and Junction Rules apply.

The Attempt at a Solution

I applied the junction rule first.

I₁ + I₂ - I₃ = 0
I₁ + I₂ = I₃

Then I applied the loop rule to the top loop.

-I₃(56) - 5 - I₁(22) = 0

And then I applied the loop rule to the bottom loop.

-I₃(56) - 1.83 - I₂(75) = 0

I know I have to use these equations to solve for the unknown I's, but I am lost on what to substitute/do next. Any insight would be great. Thanks!

 

[Delphi51]

Use I1 + I2 = I3 to replace both of the I3's in the other equations with I1 + I2.
Then you will have a system of two equations with two unknowns.
You can solve one of them for I2, then sub that into the other one to get one equation with one unknown. Alternatively, use the system solver at http://www.analyzemath.com/Calculators/Calculator_syst_eq.html to deal with the system of 2 equations.

What is the polarity on the battery symbol? Years ago they had it wrong - the small end was negative. Have they corrected that in your class or is it still that way? Of course it affects your answer so you need to know which end is positive.