WEBVTT 00:00:00.025 --> 00:00:03.170 Now, we want to solve this circuit for vx. 00:00:03.170 --> 00:00:07.790 Let's do it this particular way where we're going to use a current divider and 00:00:07.790 --> 00:00:11.110 let's find the current right here, let's call that I1 and 00:00:11.110 --> 00:00:14.710 let's find this current right here, let's call that Ix. 00:00:14.710 --> 00:00:17.920 We can say that we can find the voltage because we know the resistance. 00:00:17.920 --> 00:00:21.710 So if we do this to the current, we'd be able to find the voltage using Ohm's law. 00:00:21.710 --> 00:00:23.380 This is the current divider. 00:00:23.380 --> 00:00:26.970 When we have a current divider, the easiest way to handle that is to take 00:00:26.970 --> 00:00:31.520 our source and divide it through, let's say, R1 and R2. 00:00:32.700 --> 00:00:36.710 The current I1 and I2 is going to be found this way. 00:00:36.710 --> 00:00:41.153 Let's take our R and convert it to G, which is 1 over R1, and 00:00:41.153 --> 00:00:45.013 let's convert this one to G2, which is 1 over R2. 00:00:45.013 --> 00:00:50.158 Then we know that I1 is equal to G1 over G1 + G2, 00:00:50.158 --> 00:00:53.875 times our original source current. 00:00:53.875 --> 00:01:00.522 And I2 is equal to G2 over G1 + G2, also times our source. 00:01:00.522 --> 00:01:02.360 So let's do that over here. 00:01:02.360 --> 00:01:05.806 I can see that if I combine these two in series, that would be 12 Ohms, 00:01:05.806 --> 00:01:07.771 that's what I'll be using in that arm. 00:01:07.771 --> 00:01:11.759 So if I wanted to have G1, that would be one-third and 00:01:11.759 --> 00:01:17.090 then converting this to G2, that would be 1 divided by one-twelfth. 00:01:17.090 --> 00:01:24.868 So I1 is going to be 10 Amps times G1 over G1 + G2. 00:01:24.868 --> 00:01:30.884 I2 is going to be 10 Amps times G2 over G1 + G2. 00:01:30.884 --> 00:01:33.260 Do the math to work out what the current will be. 00:01:33.260 --> 00:01:39.090 Then because I now know I2, oops, I guess I called it x2, but 00:01:39.090 --> 00:01:47.020 there's I2, we can say that vx is going to be = I2 times the resistance which is 4. 00:01:47.020 --> 00:01:49.940 Mm-hm, let's work out the polarity on this. 00:01:49.940 --> 00:01:52.620 We can see that vx is defined from plus to minus. 00:01:52.620 --> 00:01:54.210 Let's make sure that's right. 00:01:54.210 --> 00:01:57.890 My current is defined in this direction from plus to minus, and so 00:01:57.890 --> 00:02:02.920 because these two are matching, I have the correct polarity. 00:02:02.920 --> 00:02:05.730 If I had defined my current the other direction, 00:02:05.730 --> 00:02:09.270 then I would have had a minus instead of a plus here. 00:02:09.270 --> 00:02:11.590 Okay, great, that's one way of doing this problem. 00:02:11.590 --> 00:02:13.580 Let's go do it another way. 00:02:13.580 --> 00:02:19.600 Let's say that I have the current, So here's 3, 4, and 8. 00:02:19.600 --> 00:02:22.360 And this is the voltage that I want to find. 00:02:22.360 --> 00:02:23.389 This is 10 amps. 00:02:25.782 --> 00:02:30.581 One thing that we can do is convert this thing into a voltage source and 00:02:30.581 --> 00:02:33.900 then be able to do a voltage divider. 00:02:33.900 --> 00:02:38.640 So to convert this to a voltage source, I simply say, what is the voltage across it? 00:02:38.640 --> 00:02:40.636 It's going to be 10 amps times 3. 00:02:40.636 --> 00:02:45.617 So I'm going to have a voltage source plus to minus vs of 10 times 00:02:45.617 --> 00:02:47.440 3 which is 30 volts. 00:02:48.710 --> 00:02:52.360 And then my original current this 3, that's right here, 00:02:52.360 --> 00:02:56.390 is going to end up being in series instead of in parallel. 00:02:56.390 --> 00:03:01.270 So just 3 in parallel, sorry, 3 in parallel became 3 in series. 00:03:02.280 --> 00:03:07.150 So these two things are equal, then I have my 4 Ohm and 00:03:07.150 --> 00:03:09.910 my 8 Ohm resistance, 4 and 8. 00:03:09.910 --> 00:03:12.980 And what I want to find is vx here. 00:03:12.980 --> 00:03:17.549 Remember when I have a voltage divider like so and 00:03:17.549 --> 00:03:23.131 I have a series of three resistances, R1, R2, and R3. 00:03:23.131 --> 00:03:28.964 Vs =, sorry V1 like this = vs times 00:03:28.964 --> 00:03:34.046 R1 divided by R1 + R2 + R3, 00:03:34.046 --> 00:03:39.830 similar for V2, V3, and V4. 00:03:39.830 --> 00:03:47.914 So finding xx now, I can just say that is equal to vs times 4, divided by 3 + 4 + 8. 00:03:47.914 --> 00:03:52.160 And by vs is 30 volts. 00:03:52.160 --> 00:03:56.872 So again, 30 times 4 times 3 + 4 + 8. 00:03:56.872 --> 00:03:59.700 So that's the second way of being able to solve the circuit.