1 23:59:59,500 --> 00:00:09,346 [BLANK_AUDIO]. 2 00:00:09,346 --> 00:00:13,086 In this example, we have a network of several resistors. 3 00:00:13,086 --> 00:00:15,486 And some of them are already in the configurations that are easy for us to 4 00:00:15,486 --> 00:00:20,196 analyse, but other ones are not. For example, if you look over here, where 5 00:00:20,196 --> 00:00:24,540 we have the 7 ohm resistor, the 8 ohm resistor, and the 3 ohm resistor. 6 00:00:24,540 --> 00:00:28,440 They're not directly in any simple configuration. 7 00:00:28,440 --> 00:00:30,560 Well, we don't have to do these right away. 8 00:00:30,560 --> 00:00:34,620 We can do successive implementations of the res-, the parallel resistive circuits 9 00:00:34,620 --> 00:00:38,680 that we've looked at, to work our way over to a solution. 10 00:00:38,680 --> 00:00:41,699 And so this shows us how we can do that in a multi-step process. 11 00:00:43,130 --> 00:00:45,982 So, the first thing we're going to look at is that we have this 7 ohm resistor 12 00:00:45,982 --> 00:00:49,778 here and this 8 ohm resistor here. And these two resistors are in series 13 00:00:49,778 --> 00:00:52,990 because they're not connected to anything else. 14 00:00:52,990 --> 00:00:55,075 But, they are connected to each other by this one simple node. 15 00:00:55,075 --> 00:01:03,202 So I know that the total resistance of this section [SOUND] is just the sum of 16 00:01:03,202 --> 00:01:13,870 their individual resistances. So it's 15 ohms. 17 00:01:13,870 --> 00:01:20,194 Once we've done that, we now notice that this combined resistance is now in 18 00:01:20,194 --> 00:01:27,440 parallel with this 3 ohm resistance. So we can then do a calculation of that. 19 00:01:27,440 --> 00:01:39,408 So we have 1 over 15, plus 1 over 3, to negative 1. 20 00:01:39,408 --> 00:01:44,349 Getting common denominators, 21 00:01:44,349 --> 00:01:46,545 [BLANK_AUDIO] 22 00:01:46,545 --> 00:01:58,304 6 over 15, to the negative 1. Then we can do a little bit of 23 00:01:58,304 --> 00:02:03,130 simplifying to get five halves of an ohm. [BLANK_AUDIO]. 24 00:02:09,040 --> 00:02:12,700 So now, we've found an equivalent resistance for all of that section. 25 00:02:15,700 --> 00:02:18,405 But once we know what the resistance is of that section. 26 00:02:18,405 --> 00:02:26,595 You'll notice now that is serious with this 3 half ohm resistor. 27 00:02:26,595 --> 00:02:34,155 So again, we can just sum those together, three halves plus five halves, gives us 28 00:02:34,155 --> 00:02:39,669 eight halves, or 4 ohms. That gives us this section. 29 00:02:42,660 --> 00:02:50,460 This 4 ohm resistor is now in parallel with the 12 ohm resistor. 30 00:02:50,460 --> 00:02:51,945 [BLANK_AUDIO]. So we can simply do that equation. 31 00:02:51,945 --> 00:02:55,219 [BLANK_AUDIO]. It's also interesting to notice that 32 00:02:55,219 --> 00:02:59,611 whenever you're doing parallel resistances, the total resistance will 33 00:02:59,611 --> 00:03:05,340 always be smaller than each of the individual resistances. 34 00:03:05,340 --> 00:03:06,580 So it's a good thing to check your work. [BLANK_AUDIO]. 35 00:03:13,960 --> 00:03:18,408 In this case I've got 3 ohms, which is less than 12, and it's less than 4. 36 00:03:18,408 --> 00:03:22,190 So it's probably right. With this 3 ohm resistor, this is now in 37 00:03:22,190 --> 00:03:26,718 series with this 3 ohm resistor and this 2 ohm resistor. 38 00:03:26,718 --> 00:03:31,020 So 3 plus 3 plus 2 is 8 ohms. And now that whole combination. 39 00:03:31,020 --> 00:03:35,068 Then we'll do a nice circle to keep track of where we are. 40 00:03:35,068 --> 00:03:48,152 That is all in parallel with an 8 ohm resistor. 41 00:03:48,152 --> 00:03:56,530 So we can do that, 1 over 8, and 1 over 8. 42 00:03:56,530 --> 00:04:00,151 Whenever you have two resistors that have the same resistance, and you're combining 43 00:04:00,151 --> 00:04:05,480 them in parallel like this, it's always half of the individual resistances. 44 00:04:05,480 --> 00:04:09,098 Because you always end up with having 2 over the individual resistances that you 45 00:04:09,098 --> 00:04:13,310 invert, so it's now going to be half of that 4 ohms. 46 00:04:13,310 --> 00:04:17,340 And at this point, we've just add up the remaining, because now the 7 ohm and the 47 00:04:17,340 --> 00:04:23,380 2 ohm resistor are going to be in serious with that 4 ohm equivalent resistance. 48 00:04:23,380 --> 00:04:29,160 So, 7 plus 4 plus 2 49 00:04:29,160 --> 00:04:34,200 [BLANK_AUDIO] 50 00:04:34,200 --> 00:04:36,300 [SOUND] 51 00:04:36,300 --> 00:04:43,194 is 13 ohms. [SOUND]. 52 00:04:43,194 --> 00:04:46,542 So, what we've been able to discover, is that if we go from the top node to the 53 00:04:46,542 --> 00:04:50,052 bottom node that are held open, in this particular example, we can replace the 54 00:04:50,052 --> 00:04:54,103 whole mess. All of these resistors with one single 55 00:04:54,103 --> 00:04:58,100 resistor that is 13 ohms, and we're going to get the same behavior.