[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:01.03,0:00:02.05,Default,,0000,0000,0000,,- [Voiceover] Now that\Nwe have our collection
Dialogue: 0,0:00:02.05,0:00:04.85,Default,,0000,0000,0000,,of components, our favorite\Nbatteries and resistors,
Dialogue: 0,0:00:04.85,0:00:07.56,Default,,0000,0000,0000,,we can start to assemble\Nthese into some circuits.
Dialogue: 0,0:00:07.56,0:00:09.50,Default,,0000,0000,0000,,And here's a circuit shown here.
Dialogue: 0,0:00:09.50,0:00:12.84,Default,,0000,0000,0000,,It has a battery and\Nit has three resistors,
Dialogue: 0,0:00:12.84,0:00:14.12,Default,,0000,0000,0000,,and a configuration that's called
Dialogue: 0,0:00:14.12,0:00:17.24,Default,,0000,0000,0000,,a series resistor configuration.
Dialogue: 0,0:00:17.24,0:00:19.98,Default,,0000,0000,0000,,Series resistors is a familiar pattern,
Dialogue: 0,0:00:19.98,0:00:22.49,Default,,0000,0000,0000,,and what you're looking for is resistors
Dialogue: 0,0:00:22.49,0:00:25.48,Default,,0000,0000,0000,,that are connected head\Nto tail, to head to tail.
Dialogue: 0,0:00:25.48,0:00:27.78,Default,,0000,0000,0000,,So these three resistors are in series
Dialogue: 0,0:00:27.78,0:00:31.24,Default,,0000,0000,0000,,because their succession of nodes
Dialogue: 0,0:00:31.24,0:00:33.97,Default,,0000,0000,0000,,are all connected, one after the other.
Dialogue: 0,0:00:33.97,0:00:36.96,Default,,0000,0000,0000,,So that's the pattern that tells you
Dialogue: 0,0:00:36.96,0:00:41.67,Default,,0000,0000,0000,,this is a series resistor connection.
Dialogue: 0,0:00:41.67,0:00:43.58,Default,,0000,0000,0000,,So we're gonna label\Nthese our resistors here.
Dialogue: 0,0:00:43.58,0:00:48.58,Default,,0000,0000,0000,,We'll call this R1, R2, and R3.
Dialogue: 0,0:00:49.75,0:00:51.99,Default,,0000,0000,0000,,And we'll label this as v.
Dialogue: 0,0:00:51.99,0:00:55.69,Default,,0000,0000,0000,,And the unknown in this\Nis what is the current
Dialogue: 0,0:00:55.69,0:00:58.58,Default,,0000,0000,0000,,that's flowing here, that's\Nwhat we want to know.
Dialogue: 0,0:00:58.58,0:01:01.26,Default,,0000,0000,0000,,We know v, we want to know i.
Dialogue: 0,0:01:01.26,0:01:02.92,Default,,0000,0000,0000,,Now one thing we know about i
Dialogue: 0,0:01:02.92,0:01:06.71,Default,,0000,0000,0000,,is i flows down into resistor R1,
Dialogue: 0,0:01:06.71,0:01:10.10,Default,,0000,0000,0000,,all of the current goes out of\Nthe other end of resistor R1
Dialogue: 0,0:01:10.10,0:01:13.34,Default,,0000,0000,0000,,because it has to, it\Ncan't pile up inside there.
Dialogue: 0,0:01:13.34,0:01:15.56,Default,,0000,0000,0000,,All that goes into here,
Dialogue: 0,0:01:15.56,0:01:18.28,Default,,0000,0000,0000,,and all that comes out of R3.
Dialogue: 0,0:01:18.28,0:01:23.28,Default,,0000,0000,0000,,And i returns to the place it came from,
Dialogue: 0,0:01:23.58,0:01:25.26,Default,,0000,0000,0000,,which is the battery.
Dialogue: 0,0:01:25.26,0:01:29.48,Default,,0000,0000,0000,,So that's a characteristic\Nof series resistors,
Dialogue: 0,0:01:29.48,0:01:34.48,Default,,0000,0000,0000,,is in a series configuration\Nis they are head to tail,
Dialogue: 0,0:01:41.47,0:01:44.02,Default,,0000,0000,0000,,and that means that all the components,
Dialogue: 0,0:01:44.02,0:01:49.02,Default,,0000,0000,0000,,all the resistors share the same current.
Dialogue: 0,0:01:50.94,0:01:55.53,Default,,0000,0000,0000,,Current.
Dialogue: 0,0:01:55.53,0:01:57.30,Default,,0000,0000,0000,,That's the key thing.
Dialogue: 0,0:01:57.30,0:01:58.42,Default,,0000,0000,0000,,The thing that we don't know
Dialogue: 0,0:01:58.42,0:02:00.74,Default,,0000,0000,0000,,that's different between each resistors,
Dialogue: 0,0:02:00.74,0:02:05.68,Default,,0000,0000,0000,,is the voltage here, and the voltage here,
Dialogue: 0,0:02:05.68,0:02:10.68,Default,,0000,0000,0000,,let's call that v1,\Nthis is v2, plus, minus,
Dialogue: 0,0:02:13.40,0:02:18.40,Default,,0000,0000,0000,,and this is v3, plus, minus.
Dialogue: 0,0:02:18.74,0:02:22.46,Default,,0000,0000,0000,,So in general, if these\Nresistors are different values
Dialogue: 0,0:02:22.46,0:02:24.42,Default,,0000,0000,0000,,because they have the same\Ncurrent going through them,
Dialogue: 0,0:02:24.42,0:02:28.48,Default,,0000,0000,0000,,Ohm's Law tells us these\Nvoltages will all be different.
Dialogue: 0,0:02:28.48,0:02:30.90,Default,,0000,0000,0000,,So the question I want to\Nanswer with series resistors
Dialogue: 0,0:02:30.90,0:02:34.14,Default,,0000,0000,0000,,is could I replace all three of these
Dialogue: 0,0:02:34.14,0:02:38.50,Default,,0000,0000,0000,,with a single resistor that\Ncause the same current to flow?
Dialogue: 0,0:02:38.50,0:02:41.50,Default,,0000,0000,0000,,That's the question we have\Non the table right now.
Dialogue: 0,0:02:41.50,0:02:42.98,Default,,0000,0000,0000,,So we make some observations,
Dialogue: 0,0:02:42.98,0:02:47.98,Default,,0000,0000,0000,,we have Ohm's Law, our friend, Ohm's Law.
Dialogue: 0,0:02:50.20,0:02:55.20,Default,,0000,0000,0000,,And we know that means v equals i times R,
Dialogue: 0,0:02:55.32,0:02:56.72,Default,,0000,0000,0000,,for any resistor.
Dialogue: 0,0:02:56.72,0:03:00.64,Default,,0000,0000,0000,,That sets the ratio of voltage to current.
Dialogue: 0,0:03:00.64,0:03:02.69,Default,,0000,0000,0000,,And this is another\Nthing we know about this,
Dialogue: 0,0:03:02.69,0:03:07.69,Default,,0000,0000,0000,,which is that v3, plus v2, plus v1,
Dialogue: 0,0:03:09.06,0:03:11.78,Default,,0000,0000,0000,,those are the voltages\Nacross each resistor,
Dialogue: 0,0:03:11.78,0:03:15.00,Default,,0000,0000,0000,,those three voltages have\Nto add up to this voltage
Dialogue: 0,0:03:15.00,0:03:17.72,Default,,0000,0000,0000,,because of the way the\Nwires are connected.
Dialogue: 0,0:03:17.72,0:03:21.20,Default,,0000,0000,0000,,So the main voltage from the battery
Dialogue: 0,0:03:21.20,0:03:26.20,Default,,0000,0000,0000,,equals v1, plus v2, plus v3.
Dialogue: 0,0:03:30.58,0:03:32.33,Default,,0000,0000,0000,,We know that's for sure,\Nand now what we're gonna do
Dialogue: 0,0:03:32.33,0:03:34.18,Default,,0000,0000,0000,,is we're gonna write Ohm's Law
Dialogue: 0,0:03:34.18,0:03:38.23,Default,,0000,0000,0000,,for each of these individual resistors.
Dialogue: 0,0:03:38.23,0:03:43.23,Default,,0000,0000,0000,,v1 equals i, and i is\Nthe same for everybody,
Dialogue: 0,0:03:43.71,0:03:46.57,Default,,0000,0000,0000,,times R1.
Dialogue: 0,0:03:46.57,0:03:51.57,Default,,0000,0000,0000,,v2, this voltage here, equals i times R2.
Dialogue: 0,0:03:54.26,0:03:59.26,Default,,0000,0000,0000,,And v3 equals i times R3.
Dialogue: 0,0:04:01.18,0:04:04.17,Default,,0000,0000,0000,,Now you can see, if I had four,\Nor five, or six resistors,
Dialogue: 0,0:04:04.17,0:04:07.02,Default,,0000,0000,0000,,I would have four, or five, or\Nsix equations just like this
Dialogue: 0,0:04:07.02,0:04:10.76,Default,,0000,0000,0000,,for each resistor that was in series.
Dialogue: 0,0:04:10.76,0:04:14.16,Default,,0000,0000,0000,,So now what I'm gonna do is\Nsubstitute these voltages
Dialogue: 0,0:04:14.16,0:04:17.23,Default,,0000,0000,0000,,into here, and then we'll\Nmake an observation.
Dialogue: 0,0:04:17.23,0:04:20.11,Default,,0000,0000,0000,,So let's do that substitution.
Dialogue: 0,0:04:20.11,0:04:25.11,Default,,0000,0000,0000,,I can say v equals i, R1,
Dialogue: 0,0:04:27.10,0:04:32.10,Default,,0000,0000,0000,,plus i, R2, plus i, R3.
Dialogue: 0,0:04:36.47,0:04:39.48,Default,,0000,0000,0000,,And because it's the\Nsame i on every resistor,
Dialogue: 0,0:04:39.48,0:04:44.48,Default,,0000,0000,0000,,I can write v equals i,\NI'm gonna factor out the i.
Dialogue: 0,0:04:45.40,0:04:50.40,Default,,0000,0000,0000,,R1, plus R2, plus R3.
Dialogue: 0,0:04:52.98,0:04:54.96,Default,,0000,0000,0000,,Now what I want to do\Nis take a moment here
Dialogue: 0,0:04:54.96,0:04:59.96,Default,,0000,0000,0000,,and compare this expression\Nto this one here,
Dialogue: 0,0:05:00.47,0:05:02.89,Default,,0000,0000,0000,,the original Ohm's Law.
Dialogue: 0,0:05:02.89,0:05:04.76,Default,,0000,0000,0000,,Alright, there's Ohm's Law.
Dialogue: 0,0:05:04.76,0:05:08.90,Default,,0000,0000,0000,,So we have v equals i, some current,
Dialogue: 0,0:05:08.90,0:05:12.17,Default,,0000,0000,0000,,times some resistor.
Dialogue: 0,0:05:12.17,0:05:15.14,Default,,0000,0000,0000,,I can come up with a resistor value,
Dialogue: 0,0:05:15.14,0:05:20.04,Default,,0000,0000,0000,,a single resistor that would\Ngive me the same Ohm's Law.
Dialogue: 0,0:05:20.04,0:05:25.04,Default,,0000,0000,0000,,And that is gonna be called,\Nlet's draw it over here.
Dialogue: 0,0:05:27.21,0:05:30.98,Default,,0000,0000,0000,,Here's our battery.
Dialogue: 0,0:05:30.98,0:05:35.98,Default,,0000,0000,0000,,And I'm gonna say there's a\Nresistor that I can draw here,
Dialogue: 0,0:05:37.59,0:05:42.59,Default,,0000,0000,0000,,R series, that's equivalent\Nto the three resistors here.
Dialogue: 0,0:05:44.34,0:05:48.12,Default,,0000,0000,0000,,And it's equivalent in the sense that
Dialogue: 0,0:05:48.12,0:05:52.38,Default,,0000,0000,0000,,it makes i flow here, that's\Nwhat we mean by equivalent.
Dialogue: 0,0:05:52.38,0:05:56.76,Default,,0000,0000,0000,,So in our case, to get the\Nsame current to flow there
Dialogue: 0,0:05:56.76,0:06:01.76,Default,,0000,0000,0000,,I would say v equals i times R series,
Dialogue: 0,0:06:03.76,0:06:07.76,Default,,0000,0000,0000,,in which case, what I've done\Nis I've said that R series
Dialogue: 0,0:06:07.76,0:06:10.80,Default,,0000,0000,0000,,is what, is the sum of these three things,
Dialogue: 0,0:06:10.80,0:06:15.80,Default,,0000,0000,0000,,R1 plus R2, plus R3.
Dialogue: 0,0:06:21.78,0:06:23.62,Default,,0000,0000,0000,,This is how we think\Nabout series resistors.
Dialogue: 0,0:06:23.62,0:06:27.14,Default,,0000,0000,0000,,We can replace a set of series resistors
Dialogue: 0,0:06:27.14,0:06:30.30,Default,,0000,0000,0000,,with a single resistor\Nthat's equivalent to it
Dialogue: 0,0:06:30.30,0:06:34.16,Default,,0000,0000,0000,,if we add the resistors up.
Dialogue: 0,0:06:34.16,0:06:36.80,Default,,0000,0000,0000,,Let's just do a really fast\Nexample to see how this works.
Dialogue: 0,0:06:36.80,0:06:41.80,Default,,0000,0000,0000,,I'm gonna move this screen.
Dialogue: 0,0:06:43.49,0:06:45.65,Default,,0000,0000,0000,,Here's an example with three resistors.
Dialogue: 0,0:06:45.65,0:06:50.03,Default,,0000,0000,0000,,I have labeled them 100\Nohms, 50 ohms, and 150 ohms.
Dialogue: 0,0:06:50.03,0:06:52.38,Default,,0000,0000,0000,,And what I want to know\Nis the current here.
Dialogue: 0,0:06:52.38,0:06:53.40,Default,,0000,0000,0000,,And we'll put in a voltage,
Dialogue: 0,0:06:53.40,0:06:56.96,Default,,0000,0000,0000,,let's say it's 1.5 volts,
Dialogue: 0,0:06:56.96,0:06:59.46,Default,,0000,0000,0000,,just a single small battery.
Dialogue: 0,0:06:59.46,0:07:04.16,Default,,0000,0000,0000,,So what is the equivalent resistance here?
Dialogue: 0,0:07:04.16,0:07:06.12,Default,,0000,0000,0000,,One way to figure this out\Nand to simplify the circuit
Dialogue: 0,0:07:06.12,0:07:09.83,Default,,0000,0000,0000,,is to replace all three of those resistors
Dialogue: 0,0:07:09.83,0:07:13.70,Default,,0000,0000,0000,,with a series resistor, RS,
Dialogue: 0,0:07:13.70,0:07:15.54,Default,,0000,0000,0000,,and that is, as we said here, is the sum,
Dialogue: 0,0:07:15.54,0:07:20.54,Default,,0000,0000,0000,,so it's 100, plus 50, plus 150.
Dialogue: 0,0:07:26.89,0:07:31.89,Default,,0000,0000,0000,,And that adds up to 300 ohms.
Dialogue: 0,0:07:32.69,0:07:34.70,Default,,0000,0000,0000,,So that's the value of the equivalent
Dialogue: 0,0:07:34.70,0:07:36.31,Default,,0000,0000,0000,,series resistor right here.
Dialogue: 0,0:07:36.31,0:07:41.31,Default,,0000,0000,0000,,And if I want to calculate the current, i,
Dialogue: 0,0:07:43.95,0:07:48.95,Default,,0000,0000,0000,,i equals v over R, and\Nthis case, it's R series,
Dialogue: 0,0:07:51.45,0:07:56.45,Default,,0000,0000,0000,,and that equals 1.5 divided by 300.
Dialogue: 0,0:08:00.23,0:08:03.13,Default,,0000,0000,0000,,And if I do my calculations right,
Dialogue: 0,0:08:03.13,0:08:08.13,Default,,0000,0000,0000,,that comes out to .005 amperes.
Dialogue: 0,0:08:10.66,0:08:15.66,Default,,0000,0000,0000,,Or an easier way to say it is\Nfive milliamps, milliamperes.
Dialogue: 0,0:08:20.03,0:08:22.72,Default,,0000,0000,0000,,So that's i.
Dialogue: 0,0:08:22.72,0:08:27.72,Default,,0000,0000,0000,,And now that I know i, I can\Ngo ahead and I can calculate
Dialogue: 0,0:08:29.26,0:08:32.66,Default,,0000,0000,0000,,the voltage at each point\Nacross each resistor
Dialogue: 0,0:08:32.66,0:08:35.06,Default,,0000,0000,0000,,because I know i, I know R,
Dialogue: 0,0:08:35.06,0:08:36.94,Default,,0000,0000,0000,,I can calculate v.
Dialogue: 0,0:08:36.94,0:08:41.94,Default,,0000,0000,0000,,So v1, v1, which is the\Nvoltage across that resistor,
Dialogue: 0,0:08:43.64,0:08:48.64,Default,,0000,0000,0000,,v1 equals i, R1, as we said before.
Dialogue: 0,0:08:51.62,0:08:56.62,Default,,0000,0000,0000,,So it's five milliamps\Ntimes 100 ohms, 0.5 volts.
Dialogue: 0,0:09:03.92,0:09:08.92,Default,,0000,0000,0000,,Let's do it for the other one, v2,
Dialogue: 0,0:09:12.20,0:09:17.20,Default,,0000,0000,0000,,equals i, same i, this time times R2,
Dialogue: 0,0:09:18.12,0:09:23.12,Default,,0000,0000,0000,,five milliamps times 50 ohms,
Dialogue: 0,0:09:23.85,0:09:28.85,Default,,0000,0000,0000,,and that equals 0.25 volts.
Dialogue: 0,0:09:31.30,0:09:36.30,Default,,0000,0000,0000,,And finally, we do v3.
Dialogue: 0,0:09:38.32,0:09:42.72,Default,,0000,0000,0000,,This is plus, minus v3.
Dialogue: 0,0:09:42.72,0:09:47.72,Default,,0000,0000,0000,,And that equals the same\Ncurrent again times 150 ohms,
Dialogue: 0,0:09:54.25,0:09:59.25,Default,,0000,0000,0000,,which is equal to 0.75 volts.
Dialogue: 0,0:10:01.05,0:10:03.87,Default,,0000,0000,0000,,So we've solved the\Nvoltage and the current
Dialogue: 0,0:10:03.87,0:10:06.76,Default,,0000,0000,0000,,on every resistor, so this\Ncircuit is completely solved.
Dialogue: 0,0:10:06.76,0:10:08.05,Default,,0000,0000,0000,,And let's do one final check.
Dialogue: 0,0:10:08.05,0:10:12.07,Default,,0000,0000,0000,,Let's add this up.
Dialogue: 0,0:10:12.07,0:10:15.70,Default,,0000,0000,0000,,Five, five (mumbles) is zero.
Dialogue: 0,0:10:15.70,0:10:20.45,Default,,0000,0000,0000,,Carry the one, six, seven eight.
Dialogue: 0,0:10:20.45,0:10:25.45,Default,,0000,0000,0000,,15, 1.5 volts, and that's very handy
Dialogue: 0,0:10:26.74,0:10:29.29,Default,,0000,0000,0000,,because that is the same as that.
Dialogue: 0,0:10:29.29,0:10:32.57,Default,,0000,0000,0000,,So indeed, the voltages across\Nthe resistors did add up
Dialogue: 0,0:10:32.57,0:10:37.05,Default,,0000,0000,0000,,to the full battery that was applied.
Dialogue: 0,0:10:37.05,0:10:38.59,Default,,0000,0000,0000,,There's one more thing\NI want to point out.
Dialogue: 0,0:10:38.59,0:10:43.59,Default,,0000,0000,0000,,Here's an example of\Nsome series resistors.
Dialogue: 0,0:10:46.00,0:10:47.80,Default,,0000,0000,0000,,And that's a familiar pattern.
Dialogue: 0,0:10:47.80,0:10:49.60,Default,,0000,0000,0000,,And you'll say, "Oh, those\Nare series resistors."
Dialogue: 0,0:10:49.60,0:10:53.53,Default,,0000,0000,0000,,Now, be careful because if\Nthere's a wire here going off
Dialogue: 0,0:10:53.53,0:10:56.88,Default,,0000,0000,0000,,and there's, doing this,\Nor there's a wire here,
Dialogue: 0,0:10:56.88,0:10:58.98,Default,,0000,0000,0000,,connected to this node here,
Dialogue: 0,0:10:58.98,0:11:00.39,Default,,0000,0000,0000,,this still looks like they're in series,
Dialogue: 0,0:11:00.39,0:11:02.65,Default,,0000,0000,0000,,but there might be current flowing
Dialogue: 0,0:11:02.65,0:11:04.69,Default,,0000,0000,0000,,in these branches here.
Dialogue: 0,0:11:04.69,0:11:06.73,Default,,0000,0000,0000,,If there's current flowing out
Dialogue: 0,0:11:06.73,0:11:09.25,Default,,0000,0000,0000,,anywhere along a series branch,
Dialogue: 0,0:11:09.25,0:11:12.17,Default,,0000,0000,0000,,anywhere along what looks\Nlike a series branch,
Dialogue: 0,0:11:12.17,0:11:17.17,Default,,0000,0000,0000,,then this i may or may\Nnot be the same as this i.
Dialogue: 0,0:11:17.50,0:11:20.73,Default,,0000,0000,0000,,And it might not be the same as this.
Dialogue: 0,0:11:20.73,0:11:21.76,Default,,0000,0000,0000,,So you gotta be careful here.
Dialogue: 0,0:11:21.76,0:11:25.05,Default,,0000,0000,0000,,If you see branches going\Noff your series resistors,
Dialogue: 0,0:11:25.05,0:11:30.05,Default,,0000,0000,0000,,these are not in series\Nunless these are zero current.
Dialogue: 0,0:11:31.85,0:11:35.35,Default,,0000,0000,0000,,If that's zero current, and\Nif that is zero current,
Dialogue: 0,0:11:35.35,0:11:37.92,Default,,0000,0000,0000,,then you can consider these in series.
Dialogue: 0,0:11:37.92,0:11:39.86,Default,,0000,0000,0000,,So that's just something to be careful of
Dialogue: 0,0:11:39.86,0:11:41.91,Default,,0000,0000,0000,,when you are looking at a circuit
Dialogue: 0,0:11:41.91,0:11:44.91,Default,,0000,0000,0000,,and you see things that\Nlook like they're in series,
Dialogue: 0,0:11:44.91,0:11:46.69,Default,,0000,0000,0000,,but they have little branches coming off.
Dialogue: 0,0:11:46.69,0:11:49.95,Default,,0000,0000,0000,,So a little warning there.
Dialogue: 0,0:11:49.95,0:11:51.67,Default,,0000,0000,0000,,So that's our series resistors.
Dialogue: 0,0:11:51.67,0:11:53.45,Default,,0000,0000,0000,,If you have resistors and series,
Dialogue: 0,0:11:53.45,0:11:56.54,Default,,0000,0000,0000,,you add them up to get\Nan equivalent resistance.