1 00:00:01,090 --> 00:00:05,120 Okay now we want to find Thevenin using the external voltage method, so 2 00:00:05,120 --> 00:00:10,250 our Thevenin is going to be equal to Vex/Iex. 3 00:00:10,250 --> 00:00:12,340 We do is we go back to our circuit, and 4 00:00:12,340 --> 00:00:16,250 we add in an arbitrary voltage source we can Vex. 5 00:00:16,250 --> 00:00:19,080 Since it's arbitrary, we can say it's equal to 1 volt, and 6 00:00:19,080 --> 00:00:23,530 that makes our equation very simple Then we will have an IEX. 7 00:00:23,530 --> 00:00:25,400 We don't know what that is yet. 8 00:00:25,400 --> 00:00:28,500 We solve the problem in much the same way as we did before, so watch for 9 00:00:28,500 --> 00:00:29,880 the differences. 10 00:00:29,880 --> 00:00:34,600 Our first equation is going to be VC minus 68 volts divide by 11 00:00:34,600 --> 00:00:40,040 6 ohms plus Vc minus 4 IX 12 00:00:40,040 --> 00:00:44,630 divided by 2 omes plus vc minus va, 13 00:00:44,630 --> 00:00:49,850 divided by 6 omes and that's equal to 0.No change in our first equation. 14 00:00:49,850 --> 00:00:54,465 The second equation is going to be va A minus by VC divided by 15 00:00:54,465 --> 00:00:59,735 six ohms plus VA minus zero divided by four ohms plus 16 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 17 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 18 00:01:09,375 --> 00:01:12,608 the outgoing current the current coming were going to subtract it out. 19 00:01:12,608 --> 00:01:14,925 Iex =0. 20 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 21 00:01:19,890 --> 00:01:25,305 unknown, which will be Vc-Va divided by 6 ohmes=Ix. 22 00:01:25,305 --> 00:01:30,540 Now let's take stock of our knowns and unknowns. 23 00:01:30,540 --> 00:01:36,050 We have an unknown voltage Va and Va and unknown current Ix and Iex. 24 00:01:36,050 --> 00:01:38,100 So I need one more equation. 25 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 26 00:01:41,860 --> 00:01:45,260 I can add up my ingoing and outgoing currents. 27 00:01:45,260 --> 00:01:50,190 So Ix is comming in, Iex is comming in and 28 00:01:50,190 --> 00:01:53,260 then what's going out is this current right here, let's call it I4. 29 00:01:54,710 --> 00:01:56,590 And that is going to be. 30 00:01:56,590 --> 00:02:01,460 Sorry, that's going to be equal to Va divided by four ohms. 31 00:02:01,460 --> 00:02:04,520 These are the incoming currents, that's the outgoing current. 32 00:02:04,520 --> 00:02:06,590 Then we put this together into a matrix equation, 33 00:02:08,410 --> 00:02:11,150 it's going to be a four by four matrix equation. 34 00:02:11,150 --> 00:02:17,466 So equation one, two, three, and four for unknowns Va. 35 00:02:17,466 --> 00:02:23,230 Vc, Ix, and Iex. 36 00:02:23,230 --> 00:02:27,775 My unknowns will be Va, Vc, Ix, and 37 00:02:27,775 --> 00:02:32,375 Iex and And that will have a set of four constants. 38 00:02:32,375 --> 00:02:35,335 So my first equation, what's multiplied by Va? 39 00:02:35,335 --> 00:02:37,285 It's minus one-sixth. 40 00:02:37,285 --> 00:02:38,975 What's multiplied by Vc? 41 00:02:38,975 --> 00:02:43,105 It's one-sixth plus one-half plus one-sixth. 42 00:02:43,105 --> 00:02:45,035 What's multiplied by Ix? 43 00:02:45,035 --> 00:02:46,405 Minus four halves. 44 00:02:46,405 --> 00:02:48,305 And what's multiplied by Iex0? 45 00:02:48,305 --> 00:02:49,955 What's my constant? 46 00:02:49,955 --> 00:02:50,918 Take that over there. 47 00:02:50,918 --> 00:02:53,630 It'll be 68/ 6. 48 00:02:53,630 --> 00:02:59,647 Ok second equation, lets multiply Va 1/6 Vc 49 00:02:59,647 --> 00:03:04,692 1/6, I left out a 1/4 here. 50 00:03:04,692 --> 00:03:09,800 Then minus one times I ex and nothing times no constants 51 00:03:09,800 --> 00:03:14,580 Third equation minus one sixth, Vc is one sixth and 52 00:03:14,580 --> 00:03:19,940 Ix is -1, the zero basically brought the Ix over, zero right there. 53 00:03:19,940 --> 00:03:24,730 Fourth the equation 1 times Ix, 1 times IEx, let's bring this over here, 54 00:03:24,730 --> 00:03:30,370 it will be minus one fourth and nothing times Vc and again no constant. 55 00:03:30,370 --> 00:03:35,690 When I solve this What I will find is that Iex which will come out my 56 00:03:35,690 --> 00:03:39,880 vector is going to be equal to be equal to 0.196. 57 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, 58 00:03:47,219 --> 00:03:52,394 I will find our Thevenin Is equal to, let me just invert that- 59 00:03:56,638 --> 00:03:59,450 five wholes. 60 00:03:59,450 --> 00:04:04,400 So that's how we find the Rth Thevenin using the external voltage method. 61 00:04:04,400 --> 00:04:07,180 Again we could measure, we could simulate or 62 00:04:07,180 --> 00:04:09,050 we could calculate as we did in this case.