An example
Running through an example should help clarify how Kirchoff's rules are used.
Consider the circuit below:
Step 1 of the branch current method has already been done. The currents have been
labeled in each branch of the circuit, and the directions are shown with arrows. Again,
you don't have to be sure of these directions at this point. Simply choose directions,
and if any of the currents come out to have negative signs, all it means is that the
direction of that current is opposite to the way you've shown on your diagram.
Applying step 2 of the branch current method means looking at the junctions, and
writing down a current equation. At junction a, the total current coming in to the
junction equals the total current flowing away. This gives:
at junction a : I
1
= I
2
+ I
3
If we applied the junction rule at junction b, we'd get the same equation. So, applying
the junction rule at one of the junctions is all we need to do. In some cases you will
need to get equations from more than one junction, but you'll never need to get an
equation for every junction.
There are three unknowns, the three currents, so we need to have three equations. One
came from the junction rule; the other two come from going to step 3 and applying the
loop rule. There are three loops to use in this circuit: the inside loop on the left, the
inside loop on the right, and the loop that goes all the way around the outside. We just
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 Fall '10
 DavidJudd
 Physics, Current, Kirchoff, zero volts

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