Current Dividers Explained

now let's say if we have the following circuit let's say we have two resistors parallel to each other and let's call this one let's say it's r1 and this is r2 now let's say that r1 is 4 ohms and r2 is 8 ohms and let's say the current that enters this part is 6 amps how can we calculate the current that flows through r1 and r2 now before using the formula you can figure it out intuitively notice that we have an 8 ohm resistor which is twice the value of the 4 ohm resistor so the current that flows in this branch has to be half of the current that flows through this branch because as you increase the resistance the current decreases so we need two numbers that add up to six one of which is twice the so this is going to be two and four so four amps has to flow through this resistor and two amps have to flow through the other one now it makes sense because 2 plus 4 adds up to 6 and also if you calculate the voltage across each resistor it's going to be the same for instance if we wanted to calculate the voltage across r1 based on ohm's law it's going to be the current that flows through that circuit times r1 so we have 4 amps flowing through 4 ohm resistor so 4 times 4 is 16. now if we wish to calculate volt v2 it's i2 times r2 so we have current of 2 amps flowing through an 8 ohm resistor so 2 times 8 is 16. so keep this in mind the voltage across two parallel resistors will always be the same now if you wish to use formula to calculate the current in each branch for two resistor circuit here's we can do i1 is going to equal the total current which is the six amps multiplied by the other resistor r2 divided by r1 plus r2 so this is i1 the 4 amp current let's go ahead and calculate that value is 6 amps r2 is 8 ohms and then r1 plus r2 that's going to be 4 plus 8. so this is going to be 6 times 8 divided by 12. and this will give you current of 4 amps which is the same as that value so now let's use similar formula to calculate i2 to 2 amp current so it's going to be the total current enter in the circuit multiplied by r1 divided by r1 plus r2 so it's going to be 6 amps r1 is 4 and then r1 plus r2 that's going to be 4 plus 8. so it's six times four divided by twelve and this will give us current of two amps so you can use this formula to calculate the current in such circuit so whenever the current divides into two branches and if you have the resistance of each branch you can calculate the current through each of those branches now what if we have circuit with three resistors that are parallel to each other so let's call this r1 and let's say r1 is equal to 2 ohms and r2 is going to be 4 ohms and r3 let's say it's 8 ohms and let's say the current that enters this branch is 14 amps calculate the current that flows through each resistor now the formula that you want to use in this case is going to be this one let's start with i1 i1 is going to equal the total current entering the circuit times 1 over r1 divided by 1 over r1 plus 1 over r2 plus 1 over r3 and if there's fourth resistor 1 over r4 so you can extend that equation as much as you need to this time notice that the subscripts they match and the other formula they didn't match the total current in this example is 14 amps one is two so this is going to be one over two plus one over four plus one over eight so let's go ahead and plug this in so this comes out to eight amps so that's the current that flows through r1 so i1 is 8 amps now let's calculate the current flowing through r2 using the same type of formula so i2 is going to equal the total current times 1 over r2 this time and it's going to be 1 over r1 plus 1 over r2 plus 1 over r3 and so the total current is 14 amps and r2 in this example is four now the bottom part is going to be the same it's one half plus one fourth plus one over eight now this time for those of you who may not have access to calculator i'm going to show you what to do to get the answer without calculator multiply the top and the bottom of this fraction by eight to get rid of all of the smaller fractions so if we multiply 8 by 1 4 or 8 divided by 4 that's going to equal 2 and then 8 times half half of 8 is four and then eight divided by four that's two and then eight times one over eight or eight divided by eight that's gonna be one and all of this is still multiplied to fourteen now on the bottom we have four plus two plus one which is seven so this is two over seven and fourteen is the same as seven times two so we could cancel seven and so it's two times two which gives us four so that's the current that flows through r2 it's four amps now that answer makes sense because if we compare the values of r1 and r2 notice that r2 is two times higher than r1 so if you double the resistance the current should decrease by factor of two eight divided by two is four and so that makes sense now to calculate the missing current we can use this fact the total current is the sum of the individual currents in this parallel circuit so the total current is 14 amps i1 is 8 i2 is 4 so now we can calculate i3 8 plus 4 is 12 and 14 minus 12 is 2. so the current flowing through this branch is 2 amps now if we compare the 8 ohm resistor and the 4 ohm resistor going from r2 to r3 we're increasing the resistance by factor of 2. so going from i2 to i3 we should decrease the current by factor 2. 4 divided by 2 will give us this answer so there's other ways in which you can find the other missing currency if you know one of them now this time we're going to have network of four resistors as opposed to just three so let's say the current that enters this circuit is 15 amps and let's say r1 that's going to be 12 ohms r2 let's make that 24 ohms and then r3 we're going to say it's 16 ohms and r4 is going to be 8 ohms so calculate the current flowing through every branch of that parallel circuit so let's start with current one it's going to equal the total current times 1 over r1 divided by 1 over r1 plus 1 over r2 plus 1 over r3 plus 1 over r4 so the total current is 15 and r1 is 12 so we're going to have 1 over 12. on the bottom it's going to be 1 over 12 plus 1 over r2 which is 1 over 24 and then 1 over r3 and then 1 over r4 which is 1 over 8. so now let's get the answer without using the calculator so i'm going to multiply the top and the bottom by the common denominator or the least common multiple of 12 24 16 and 8. so all of these numbers can go into 48 so i'm going to multiply the top and the bottom by 48. so 48 divided by 12 is 4 and have 15 in front of that and so 1 over 12 times 48 that's going to be 4 again and then 1 over 24 times 48 or 48 divided by 24 that's 2 48 divided by 16 is 3 and 48 divided by 8 is 6. now let's add up the numbers in the denominator so four plus two is six six plus three is nine nine plus six is fifteen and so we could cancel the fifteen therefore the current that flows through r1 is 4 amps now let's calculate the current that flows through r2 you could use the same formula but you don't need to once you find one of the currents it's going to be easy to find the rest so let's compare r1 and r2 notice that the resistance increases from 12 to 24. so if you compare two resistors in parallel if one of the resistors doubles in value then the current of the other one the one with the high resistance has to be half of the current with the smaller resistance so to calculate the other current it's going to be 4 divided by 2 so 2 amps so anytime you double resistor in parallel circuit the current flowing through that resistor is going to be half compared to the other resistor that have half the resistance now let's calculate the current flowing through r3 another thing you need to keep in mind is that the voltage across each resistor is the same so v1 is equal to v2 which is equal to v3 and that's equal to v4 so let's calculate v1 that's i1 times r1 so we have current of 4 amps flowing through 12 ohm resistor and 4 times 12 is 48. so v1 v2 v3 all of them is equal to 48. so now v3 is equal to i3 times r3 so we could find the current that's flowing through this resistor by taking the voltage and dividing it by the resistance so the voltage is 48 volts and we're going to divide it by 16 ohms so that's gonna be three amps so that's the current that flows through the third resistor now to calculate the last current we can use this equation the total current is the sum of all four currents in this circuit so the total current is 15. i1 is 4 i2 is 2 i3 is 3 and that let's calculate i4 so 4 plus 2 is 6 6 plus 3 is 9. so we have 15 is equal to 9 plus i4 so i4 is going to be 15 minus 9 which equals 6 amps so now we have the current flowing through every resistor and to check the work we know that v1 equals v2 which equals v3 which equals v4 so what that means is that the products of the current and resistance have to all equal each other so if we multiply 4 by 12 that will give us 48 2 times 24 is also 48 3 times 16 is 48 and 6 times 8 is 48 so each resistor has the same voltage across each of them when they're connected in parallel and so now you know how to calculate the current of every resistor in parallel circuit if you're given the total current that enters that circuit so thanks again for watching you