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Example: Analyzing a more complex resistor circuit

Video transcript

let's see if we can apply what we've learned to a particularly hairy problem that I have constructed so let's say let me see how I can construct this okay so let's say in parallel I have this resistor up here and I try to make it to the numbers work out reasonably neat that is for ohms then I have another resistor right here that is 8 ohms then I have another resistor right here that is 16 ohms and then I have another resistor here it's ohms actually I'm now making it up on the fly I think the numbers might work out ok 16 ohms let's say that now here in series I have a resistor that is let's say it is 1 ohm and then in parallel to this whole thing now you can see how hairy it's getting I have a resistor that is I don't know let's say 3 ohms 3 ohms and let's say I have a resistor here I don't let's just make it simple 1 ohm and I know just to make the numbers reasonably easy I am doing this on the fly now that's the positive terminal negative terminal let's say that the voltage difference is I don't know 20 volts so what I want us to do is figure out what is the current flowing through the wire at that point right now for obviously that's going to be different than the current at that point that point that point that point all of these different points but it's going to be the same as a current flowing at this point so what is I so the easiest way to do this is try to figure out the equivalent resistance because once we know the equivalent resistance of this big hairball then we can just use Ohm's law and be done so first of all let's just start at we I could argue the simplest part let's see if we could figure out the equivalent resistance of these four resistors in parallel well we know that that resistance is going to be equal to 1 over 4 plus 1 over 8 plus 1 over 16 plus 1 over 16 so that resistance now it's just adding fractions over 16 1 over 4 is 4 over 16 plus 2 over 16 plus 1 plus 1 so 1 over r is equal to 4 plus 2 is equal to 8 over 16 the numbers are working out is equal to 1/2 so that equivalent resistance is 2 so that quickly we just said well all of these resistors combined is equal to 2 ohms so let me erase that and simplify our drawing simplify it so that whole thing that whole thing could now be simplified as 2 ohms let me draw I lost some wire here don't want to open want to make sure the circuit can still flow so that easily I turn that big hairy mess into something that is a lot less hairy well what is the equivalent resistance of this resistor and this resistor well they're in series and series resistors they just add up together right so the combined resistance of this 2 ohm resistor and this 1 ohm resistor is just a 3 ohm resistor so let's erase and simplify so then we get that combined resistor right we had a 1 we had a the 2 ohm that we had simplified and we had a 1 ohm and whoops I'm using the wrong color so we had a 2 ohm in a wall mode on the series of those simplify to 3 ohms well now this is getting really simple so what do what do these two resistors simplify to well 1 over their combined resistance is equal to one over three plus one over three it equals what two over three one over R is equal to two over three so R is equal to three halves or I don't know we could say 1.5 right so let's erase that and simplify simplify our drawing so this whole mess this this the combined the R is it a three ohm resistor and probably another three ohm resistor is equal to one resistor with a 1.5 resistance and then and and actually this is actually good point to give you a little intuition right because even though these are three ohm resistors we have two of them so it's kind of giving it you're kind of increasing the pipe that the electrons can go in by a factor of two right so it's actually decreasing the resistance it's giving more avenues for the electrons to go through actually they're going to be going in that direction and that's why the combined resistance of both of these in parallel is actually half of either one of these resistance I encourage you to think about that some more give you some intuition of what's actually going on with the electron although I'll do a whole video on resistivity okay so let's we said those two resistors combined I wanted to lead all of that those two resistors combined equal to 1.5 ohm resistor that's one point five ohms and now all we're left with is two resistors in parallel so the whole circuit becomes this which is the very basic one this is a resistor 1 point 5 ohms 1 ohm in series did I say perilous now no they're in series 1 point 5 plus 1 that's 2 point 5 ohms 2 point 5 ohms the voltage is 20 volts across them so what is the current Ohm's law V is equal to I R voltage is 20 is equal to current times R equivalent resistance times 2 point 5 ohms or another way to write 2.5 is 5 halves all right so 20 is equal to I times 5 halves or I is equal to two fifths times 20 and what is that 2/5 is equal to I is equal to 8 8 and peers that was not so bad I don't think although when you saw it initially it probably looked extremely intimidating anyway if you understood that you can actually solve fairly complicated circuit problems I will see you in future videos