WEBVTT 00:00:01.090 --> 00:00:05.120 Okay now we want to find Thevenin using the external voltage method, so 00:00:05.120 --> 00:00:10.250 our Thevenin is going to be equal to Vex/Iex. 00:00:10.250 --> 00:00:12.340 We do is we go back to our circuit, and 00:00:12.340 --> 00:00:16.250 we add in an arbitrary voltage source we can Vex. 00:00:16.250 --> 00:00:19.080 Since it's arbitrary, we can say it's equal to 1 volt, and 00:00:19.080 --> 00:00:23.530 that makes our equation very simple Then we will have an IEX. 00:00:23.530 --> 00:00:25.400 We don't know what that is yet. 00:00:25.400 --> 00:00:28.500 We solve the problem in much the same way as we did before, so watch for 00:00:28.500 --> 00:00:29.880 the differences. 00:00:29.880 --> 00:00:34.600 Our first equation is going to be VC minus 68 volts divide by 00:00:34.600 --> 00:00:40.040 6 ohms plus Vc minus 4 IX 00:00:40.040 --> 00:00:44.630 divided by 2 omes plus vc minus va, 00:00:44.630 --> 00:00:49.850 divided by 6 omes and that's equal to 0.No change in our first equation. 00:00:49.850 --> 00:00:54.465 The second equation is going to be va A minus by VC divided by 00:00:54.465 --> 00:00:59.735 six ohms plus VA minus zero divided by four ohms plus 00:00:59.735 --> 00:01:04.694 alright if I had done BA minus BEX I would of had to divide by zero because there's 00:01:04.694 --> 00:01:09.375 zero resistance in this arm instead what I'm going to do is I'm going to add in 00:01:09.375 --> 00:01:12.608 the outgoing current the current coming were going to subtract it out. 00:01:12.608 --> 00:01:14.925 Iex =0. 00:01:14.925 --> 00:01:19.890 Our third equation is going to be the same we had before in order to find our Ix 00:01:19.890 --> 00:01:25.305 unknown, which will be Vc-Va divided by 6 ohmes=Ix. 00:01:25.305 --> 00:01:30.540 Now let's take stock of our knowns and unknowns. 00:01:30.540 --> 00:01:36.050 We have an unknown voltage Va and Va and unknown current Ix and Iex. 00:01:36.050 --> 00:01:38.100 So I need one more equation. 00:01:38.100 --> 00:01:41.860 Well since this is a current I'm looking for let's just put a note right here and 00:01:41.860 --> 00:01:45.260 I can add up my ingoing and outgoing currents. 00:01:45.260 --> 00:01:50.190 So Ix is comming in, Iex is comming in and 00:01:50.190 --> 00:01:53.260 then what's going out is this current right here, let's call it I4. 00:01:54.710 --> 00:01:56.590 And that is going to be. 00:01:56.590 --> 00:02:01.460 Sorry, that's going to be equal to Va divided by four ohms. 00:02:01.460 --> 00:02:04.520 These are the incoming currents, that's the outgoing current. 00:02:04.520 --> 00:02:06.590 Then we put this together into a matrix equation, 00:02:08.410 --> 00:02:11.150 it's going to be a four by four matrix equation. 00:02:11.150 --> 00:02:17.466 So equation one, two, three, and four for unknowns Va. 00:02:17.466 --> 00:02:23.230 Vc, Ix, and Iex. 00:02:23.230 --> 00:02:27.775 My unknowns will be Va, Vc, Ix, and 00:02:27.775 --> 00:02:32.375 Iex and And that will have a set of four constants. 00:02:32.375 --> 00:02:35.335 So my first equation, what's multiplied by Va? 00:02:35.335 --> 00:02:37.285 It's minus one-sixth. 00:02:37.285 --> 00:02:38.975 What's multiplied by Vc? 00:02:38.975 --> 00:02:43.105 It's one-sixth plus one-half plus one-sixth. 00:02:43.105 --> 00:02:45.035 What's multiplied by Ix? 00:02:45.035 --> 00:02:46.405 Minus four halves. 00:02:46.405 --> 00:02:48.305 And what's multiplied by Iex0? 00:02:48.305 --> 00:02:49.955 What's my constant? 00:02:49.955 --> 00:02:50.918 Take that over there. 00:02:50.918 --> 00:02:53.630 It'll be 68/ 6. 00:02:53.630 --> 00:02:59.647 Ok second equation, lets multiply Va 1/6 Vc 00:02:59.647 --> 00:03:04.692 1/6, I left out a 1/4 here. 00:03:04.692 --> 00:03:09.800 Then minus one times I ex and nothing times no constants 00:03:09.800 --> 00:03:14.580 Third equation minus one sixth, Vc is one sixth and 00:03:14.580 --> 00:03:19.940 Ix is -1, the zero basically brought the Ix over, zero right there. 00:03:19.940 --> 00:03:24.730 Fourth the equation 1 times Ix, 1 times IEx, let's bring this over here, 00:03:24.730 --> 00:03:30.370 it will be minus one fourth and nothing times Vc and again no constant. 00:03:30.370 --> 00:03:35.690 When I solve this What I will find is that Iex which will come out my 00:03:35.690 --> 00:03:39.880 vector is going to be equal to be equal to 0.196. 00:03:39.880 --> 00:03:47.219 Then, when I take our Thevenin which is equal to Vex which was 1 divided by 0.196, 00:03:47.219 --> 00:03:52.394 I will find our Thevenin Is equal to, let me just invert that- 00:03:56.638 --> 00:03:59.450 five wholes. 00:03:59.450 --> 00:04:04.400 So that's how we find the Rth Thevenin using the external voltage method. 00:04:04.400 --> 00:04:07.180 Again we could measure, we could simulate or 00:04:07.180 --> 00:04:09.050 we could calculate as we did in this case.