00:01
All right, hello.
00:01
In this question, we're given this setup, where we have a circuit.
00:04
We got three resistors, two voltage sources.
00:07
And we're told all of the values.
00:08
And we're said to write kirchhoff's equations for the upper loop, outer loop, lower loop, and then also the equation for the currents, the disjunction rule, and then determine the currents flowing through the resistors, respectively.
00:24
So let's go ahead and start with the outer loop, because that's what we're interested in, i suppose.
00:30
That's the first one i'd ask.
00:31
So i'm going to start in the bottom right.
00:32
And i'm going to go ahead and go in that direction.
00:35
So if i start here and go through ir3, well, since my arrow is pointing in the same direction as my current in the clockwise direction, i'm going to have minus i3 times r3, which is 10.
00:49
And then i'm going to go out.
00:52
And i'm going to go from plus to minus.
00:54
So i'm going to lose 5 volts at that source.
00:57
And then i'm going to go backwards against my i1 arrow.
01:00
So i'm going to have plus i1 times 4.
01:04
And i'm going to be very loose here with the sig figs, just because there's a lot of writing and math to be done.
01:09
And it makes it a lot easier.
01:11
And then i go, if i continue, i'm going to end up back where i started.
01:14
So that's going to equal zero.
01:16
Let's go ahead and do the upper loop, starting again in the bottom right part.
01:20
So i'm going to go from minus to plus on the 8 volts.
01:23
So i'm going to have plus 8 volts minus i2 times 8, because i'm going with i2's direction.
01:29
And i'm going from plus to minus.
01:30
So i'm going to lose 5 volts at this source here.
01:34
And i'm going opposed to i1.
01:36
So i'm going to have plus i1 times 4.
01:39
And then i'm back where i started.
01:40
So that equals zero.
01:42
For the bottom loop here, i'm going to do it in blue.
01:45
While i go through i3, which has a resistance of 10 ohms...