00:01
All right, so to find the current through each of these resistors and the current through the battery, we first need to figure out the equivalent resistance.
00:10
And we can do that by looking at each of the parallel resistors first.
00:16
The equivalent resistance of resistors in parallel can be found by using the one over rule.
00:22
So we have the reciprocal of our equivalent, and we set that equal to one over each of these resistors added together.
00:32
So one over r1, or sorry, one over r2 plus one over r3 plus one over r4.
00:38
And so it's the reciprocal of each resistor added together, and then you take the sum of them and then take the reciprocal of that.
00:46
So our equivalent will be one over r2, which is 10 .4, plus one over r3, which is 26, plus one over r4, which is 15 .6.
01:01
So we take those reciprocals and we get 0 .1987, which is really close to 0 .2.
01:12
And so then we take the reciprocal of that and we get our equivalent as 5 .03.
01:20
So 5 .03 ohms is the equivalent resistor of the resistors in parallel.
01:26
So that's these three resistors in parallel.
01:30
Now we can find the total resistance by just adding to that r1.
01:36
So r total is r1 plus r equivalent.
01:44
And so that's 5 .2 plus 5 .03.
01:48
So we get 10 .23.
01:50
Now that we have r total, we can find the current through the battery, which is going to be the same as the current through r1.
02:00
So i1 will be the current through r1 as well as the current through the total.
02:10
So 12 over 10 .23, and we get a current of 1 .17 amps.
02:20
Now the voltage drop across r2, r3, and r4 will all be the same, and it will be less the voltage drop across r1...