00:01
So in this problem, we're looking for the value of two currents running through this circuit in different branches, i2 and i3.
00:09
And when we have a problem like this, a circuit that's set up like this, we can apply the loophole, which states that the sum of the potential differences across a loop in a circuit should equal zero once you complete that loop.
00:21
And we can also apply the junction rule, which states that the current coming into a junction should be equal to the current coming out.
00:28
So if we start by applying the junction rule, we can see here that i1 is going to be equal to i2 plus i3, since these are the currents that are coming out, and i1 is the current that's coming into that particular junction.
00:45
Now if we go ahead and apply the loop rule to the outer loop, we'll have an expression that looks like this.
00:51
We'll have 12 minus .01 times i1 minus .06, times i3, and that'll be equal to 0.
01:06
And if we apply the loop rule again to the right loop, we'll get an expression that looks like this.
01:13
We'll have 10 plus i2 minus 0 .06 times i3, all equal to 0.
01:25
So now what we can do is we can substitute i1 with i2 plus i3 into the second equation.
01:32
So we'll go ahead and substitute in that, which will give us a modified expression for equation 2.
01:42
We'll just go ahead and label these equations so we know which ones we're talking about...