ShmoopTube

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And here's your shmoop du jour brought to you by cupcakes because we

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love bite-sized desserts whether they're supposed to be bite-sized or not let it [Woman swallows cupcake]

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go Louis said his mother let it go no way

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Louise would not rest until justice was served minutes earlier he had opened the

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cupboard to find that his cupcake was missing Louise began his investigation [Luis opens cupboard]

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he lined up the usual suspects dad and Fido no one was talking or barking his

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case was colder than a penguin at the Winter Olympic then Luis remembered [Penguin skiing]

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something that might blow this case wide open the cops on that TV show had used a

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lie detector so Luis built one for himself [Luis with a lie detector]

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he hooked the suspects up one by one phyto just wagged his tail [Fido performing lie detector test]

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dad denied the crime at first but for the questioning broke him he mumbled and

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hesitated a single bead of sweat running down his face the buzzer sounded so we [Dad sweating while doing lie detector test]

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could barely believe it cupcake crossed by his own father okay take a look at

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the following diagram yeah this lie-detector a circuit took advantage of [Lie detector circuit diagram appears]

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a suspect physical inability to lie a moist finger from a sweaty skinned liar

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would complete the circuit and ring the buzzer when the circuit is completed

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what current flows through the 750 ohm resistor assume that the buzzards

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resistance can be ignored all right here is potential answer.....

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we appreciate Luis quest for justice here but he probably could have baked a [Luis in a classroom]

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dozen cupcakes in the time it took him to rig this thing up however it's the

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principle of the thing that matters plus it's pretty sweet to get your dad

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red-handed that's assuming it was a red velvet [Dad with red hand and red velvet cake appears]

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cupcake of course in this circuit we have 1.5 volt batteries with a total

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potential difference of three volts let's figure out the resistance we're

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dealing with first we have four resistors here two of them are in series

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so we can add those up to get a total resistance of 1500 ohms in that section

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of the circuit now we have two resistors in parallel to calculate total [Finger points to resistors on diagram]

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resistance in parallel resistors we need add the reciprocals of the resistances

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then find the reciprocal of that sum and it looks like this now if we only have [Parallel resistance formula appears]

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two parallel resistors we can also find the answer by multiplying your

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resistances then dividing that by their sum no matter how we do the math the

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answer is the same which is good because that's kind of how math is supposed to

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work we have a total resistance of 500 ohms for this part of the circuit so now [Finger points to circuit]

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we can look at the circuit as having two resistors in series one of 500 ohms and

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one of a thousand ohm and we can add that to find a total resistance of 1500

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ohm all right now we're getting somewhere

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we can find the current using Ohm's law which states that the current equals [Ohm's law appears]

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volts divided by resistance well in this case we have three volts and fifteen

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hundred ohms giving us a current of two milliamps now to be frank at this point

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we've pretty much forgotten what's question was in the first place but [Man scratches head]

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looking back we're supposed to find the amount of current that's flowing through

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the 750 ohm resistor there we go since one part of this Junction has a

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resistance of 1500 ohms and the other has half of that 750 ohms [Arrow points to resistances]

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yeah that's paths we know that twice as much current flows through the 750 ohm

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resistance well we can look at it like this the total current equals 2I plus

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I giving a total of three I that equals the current two milliamps

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well one third of the current goes through the 1500 ohm resistance and we

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double that to find the portion of current that flows through the 750 ohm

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resistor which means the correct answer is d and if this situation ever happens

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again well let's save everyone a whole lot of trouble and just chip in by [Dad gives Luis a cupcake]

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Luis another cupcake

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