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# Parallel resistors (part 2)

## Video transcript

in the last video we introduced the idea of parallel resistors these two resistors are in parallel with each other because they share nodes and they have the same voltage across them so that configuration is called the parallel resistor and we also showed that these two resistors could be replaced by a single resistor we label this one r1 this is r2 we show that we can replace r1 and r2 by an equivalent parallel resistor with this expression here for two resistors R P 1 over R P equals 1 over r1 plus 1 over r2 so that's how you calculate the equivalent resistance for two parallel resistors now you can ask and it's a good thing to ask what if there's more resistors what if there's more resistors in parallel here what if I have r3 and r4 and RN all connected up here what happens to this expression so like we did before we had a current here and we know that current comes back here ah the first current split some current goes down through r1 some goes through r2 and if we had more resistors some goes down through our three as some goes down through RN so the current basically is coming down here and splitting amongst all the resistors now all the resistors share the same all the resistors share the same voltage so that's just V let's label V that's just V they all shares the same V and they all have a different current assuming they all have a different resistance value so we do exactly the same analysis that we did before which was we we know that I here has to be the sum there's the summation symbol of all the I's I 1 plus I 2 plus I 3 plus I and that's as many as we have so we know that's true and we also know that the current we also know that the current in each individual resistor I n is equal to 1 over that resistor times V and V is the same for every one of them so now we substitute this equation into here for I I for I we get the bigeye the overall I is equal to voltage times it's going to be a big expression 1 over r1 plus one over r2 plus one over r3 plus as many resistors as we have one over r-n like that and we do the same thing it was we did before which was we say this expression here is equivalent to one parallel resistor we're going to make that equal to one parallel resistors so this whole guy here is going to become one over RP that gives us a way to simplify any number of resistors down to a single parallel resistor and I'll write that over here so for an resistors multiple resistors one over RP the equivalent parallel resistor is equal to the same thing 1 over r1 plus 1 over r2 plus dot dot dot one over R n so this tells you how to simplify any number of parallel resistors down to one equivalent parallel resistor