Series and Parallel Circuits: A Water Analogy - Free Educational videos for Students in K-12

Series and Parallel Circuits: A Water Analogy - By MITK12Videos

Transcript


00:06	Hi today , we're going to discuss series and parallel
00:09	circuits and to do so , we're using a water
00:11	analogy . We use the water analogy because we can
00:16	see water and it's very hard to see electrons and
00:18	how electrons flow through a circuit . Now , let's
00:21	go in the lab and explore how we made this
00:23	analogy . Come to life . Here we are designing
00:26	resistors that will be used in this demonstration . This
00:29	laser cutters cutting out water resistors from a plastic sheet
00:32	. The resistors have four small holes and they restrict
00:35	the flow of water . Here we are adding give
00:37	resistor to the tube that slows down the flow of
00:39	water . Here we are building our water circuit will
00:45	use these two liter bottles to show how the water
00:47	level changes as a result of resistors in the tubes
00:51	. This is the first circuit we're going to explore
00:53	. It's pretty simple . We have two resistors in
00:56	series and we're going to look at how the water
00:57	level changes across the resistors . Now we're going to
01:00	simulate this circuit using water instead of electricity , we
01:03	put a two liter bottle at each of the black
01:05	dots of the circuit to visualize the change in water
01:08	level . The voltage in this diagram is related to
01:11	the total water height in the two liter bottles of
01:13	our water circuit . So here's the first resistor placed
01:17	in the left tube , and here's the second resistor
01:19	placed in the right tube , and now we're going
01:21	to fill up this two liter bottle on the right
01:23	. In the water analogy represents our voltage source by
01:25	filling it up with water . We're putting pressure on
01:27	the line and this pressure causes water current to flow
01:29	through the tube across the resistor and into the middle
01:32	two liter bottle . There must be a pressure difference
01:34	across the resistor in order for current flow for current
01:37	to flow through the left resistor . A pressure difference
01:40	must build up the water fills the middle to later
01:42	bottle . The water level of the middle bottle stabilizes
01:45	. When the flow of water coming into the bottle
01:47	from the right resistor equals the flow of water leaving
01:49	the bottle from the left resistor . Now let's mark
01:52	this water level so that we can later compare it
01:54	to different resistor arrangements . The flow of electric charges
01:58	called electric current because it brings to mind the flow
02:01	of water , which is also called current , in
02:04	which we are also very familiar with . The voltage
02:08	V is a measure of the pressure provided to the
02:10	electrons so that they can move in water if you
02:13	have two containers at the same level and you connect
02:16	them with a tube . No current flows between them
02:19	as there is no pressure difference , the voltage is
02:21	zero , but if you have two containers at different
02:24	levels and connect them with a tube , there is
02:27	a pressure difference between them and current flows from higher
02:30	pressure to lower pressure . The resistor r can be
02:35	thought of as obstacles to current flow such as boulders
02:38	in a river . Current two liter bottles were positioned
02:42	at the locations of the three black dots . The
02:45	total current flowing through the circuit is given by I
02:48	. Total which equals the voltage V divided by the
02:51	equivalent resistance . The equivalent resistance R . E .
02:55	Q . For the series resistors add together so R
02:58	. E . Q equals R plus R which equals
03:01	to our I . Total can be written as V
03:05	divided by two are then we cannot solve for the
03:08	middle which equals I total times are since we just
03:12	solve for I total , we can plug that into
03:14	the equation and we get the middle equals the divided
03:17	by two R . Times R . Which equals V
03:21	. Over to this means that we'd expect the water
03:23	height at the middle of the circuit to equal half
03:26	of the total water height of the pressure source .
03:28	On the right . From the experiment we find a
03:31	very similar result for the second circuit . We have
03:35	a parallel component and a serious component . The parallel
03:39	part is on the right where there are two tubes
03:42	, each with a single resistor connected in parallel .
03:45	And on the left we have a single tube with
03:47	a single resistor just as before . And it is
03:50	in series with the parallel circuit on the right .
03:54	So here's a little derivation for the equivalent resistance for
03:57	resistors in parallel . That might help you remember the
04:00	formula . So here I'm drawing two resistors in parallel
04:03	. R . one and R . two . The
04:05	current going through resistor R one is I want in
04:08	the current going through resistor . R two is I
04:11	. Two . And there's a voltage across the resistors
04:14	. V . and the total current through the circuit
04:16	is I . Total which equals I one plus I
04:19	to but each resistor only sees the voltage source .
04:23	It doesn't know that the other resistors there . So
04:26	we can just draw your transistor separately which gives I
04:29	one equals V over R . One and I two
04:32	equals V over R . Two . I said before
04:35	I totally equals I one plus I to we can
04:38	write a total as the voltage v divided by some
04:42	equivalent resistor . R . E . Q . So
04:45	if we write it out like this we can see
04:47	that we can easily derive the formula for equivalent resistor
04:51	by substituting the expressions for I one and I two
04:55	from the equations at the top right . We see
04:57	that one over R . E . Q . Equals
05:00	one over R . One plus one over R .
05:02	Two . So as we fill the right bottle up
05:06	with water once again we're providing a pressure difference that
05:08	causes water current to flow . The middle two liter
05:11	bottle begins to fill with water , but will the
05:13	water filled to a level that is higher or lower
05:16	than the previous circuit ? Let's see Here we solve
05:20	circuit two . The three white dots represent the two
05:23	liter bottles in our water circuit . We want to
05:25	solve for the middle , which will tell us the
05:27	water height of the middle two liter bottle compared to
05:30	the full two liter bottle on the right , which
05:32	acts as our water pressure source . Will first reduce
05:35	the parallel component of the circuit to an equivalent resistor
05:38	from before we know that the formula for these two
05:40	resistors in parallel is one over our equivalent equals one
05:45	over R plus one over R . Which equals two
05:47	over our . That gives R . E . Q
05:50	equals R . Over to . Now . We redraw
05:52	the circuit and we replaced the parallel component with the
05:55	equivalent resistor . We just calculated once we make this
05:58	substitution , it's a simple circuit to solve similar to
06:01	circuit one . R E . Q . For this
06:03	circuit is R plus R . Over two equals three
06:07	half times . Are I total equals V over R
06:11	. E . Q . Which equals the divided by
06:14	three halfs times are and this gives the middle equals
06:18	I . Total times are and we substitute in for
06:21	I total and get that that equals the divided by
06:25	three half times are times are Which equals 2/3 times
06:30	v . Therefore we expect the water level of the
06:32	middle two liter bottle to be approximately two thirds the
06:35	height of the bottle on the right . Let's see
06:37	what happens . We see that the water level of
06:41	the middle bottle has risen to a level that is
06:43	higher than the level of circuit one we mark it
06:46	with appeared to indicate that this is the water level
06:48	for the parallel circuit . And here's the third circuit
06:52	we're going to look at . In this case we
06:54	placed two resistors in series and the right to .
06:57	These resistors are also in series with a resistor in
07:00	the left to so there's a resistor on the left
07:04	tube and here are the two resistors placed in series
07:06	and the right to we're filling up the right bottle
07:08	with water to create a pressure difference to cause water
07:11	current to flow . How high will the water fill
07:13	the middle bottle ? Will it be higher or lower
07:15	than circuit one ? In Circuit Two . Let's see
07:20	the diagram for circuit three is shown and it is
07:22	similar to circuit what we saw for I total equals
07:25	V . Divided by some equivalent resistor which equals V
07:28	divided by three times . Are . Remember resistors add
07:31	in series so R . E . Q equals R
07:34	plus R plus R . Which equals three are the
07:37	middle equals I . Total times are and we plug
07:39	in V divided by three times are for I total
07:42	which we just calculated this gives that the middle should
07:44	equal V . Divided by three or the height of
07:46	the water in the middle two liter bottles should be
07:49	about one third the height of the bottle on the
07:51	right . We see that the water level of the
07:54	middle bottle has risen to a level much lower than
07:56	the circuit one and two . We marked the level
07:59	with an S . To indicate that this is the
08:00	series combination circuit . We hope you enjoyed the lesson
08:04	. Thanks

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