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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