00:01
Here we're given a circuit with a lot of unknown currents and potentials.
00:07
They're asking us first to define and determine all the currents.
00:11
So i'm going to do this in no particular order.
00:14
I'm going to use my loop rule right here with our power supply, knowing that in this loop the voltage goes up 20 volts, and so it has to go down 20 volts, which means the potential difference across resistor 3.
00:31
Is 20 volts and therefore the current through resistor 3 by olms law 20 over 5 is 4 amps there's one similarly i'll do another loop rule over here this shows that i can turn that into a loop rule equation where the potential difference across one, about across resistor one plus the potential difference across resistor two is going to be equal to 20 volts, which is not immediately helpful right now, but will be later maybe.
01:31
I'm going to draw another loop.
01:33
I'll call this the green one, where i'm going to go this way.
01:39
So again, i can write an equation for the potential difference across resistor 5 plus the potential difference across resistor 4 plus the potential difference across resistor 1 is equal to our 20 volts.
02:01
And from this, we can kind of see that the potential difference across resistor 2 is going to be the same as the potential difference across.
02:14
Resistor 4 and 5 together kind of because they're in parallel in some capacity all right so i'm going to simplify this circuit a little bit i'm going to kind of take this chunk of the circuit and redraw it in a simplified manner so i'm still going to have my battery over here i still have this guy up here i still have r1 over here.
02:48
This is 10 oms, 5 oms, 20 volts.
02:54
But instead i'm going to have, and these are like one point.
03:01
So i'm going to try to take that thing that i circled in yellow and simplify it.
03:08
So it looks like i've got a 20 -oom resistor, right, in parallel with a 14 and a 6 that are in series.
03:16
So the 14 and the 6 combined to become 20 just by resistors in series.
03:22
Now if i have a 20 om and a 20 om in parallel, that simplifies to a 10 om by adding resistors in parallel.
03:33
So this is a 10 -on equivalent.
03:35
And now this will help me simplify my circuit a little more.
03:40
And so here i've got, with a simpler circuit, i can go even further and combine some where those are in series so those become a 20 om equivalent and now i've got a 20 om and a 5 om in parallel so i can quickly do my resistors in a parallel formula to get the total resistance of the whole circuit and that'll help me find the total current so if i do this this equals 1 over 20 plus 4 over 20 so the resistance of the whole circuit is 20 so if i know the total is 4 oms, i know my voltage total is 20 volts.
04:38
I know my total current in the circuit, which is also equal to is, how they've defined it, the current through the power source, is going to be equal to 5 amps.
04:50
So now, right, i'm just given that the current going through here is equal to 5 amps.
05:00
And so now we can use the junction rule to help us solve for some currents.
05:06
So if i know 5 amps enters this junction here, right, i know that 4 amps come through this way, 4 amps eventually go down that way.
05:19
Here we're given a complex circuit, some resistors, one power source, and they define this point as the ground point, the grounding point there.
05:33
And we're asked to determine the currents through most of the resistors given here.
05:43
I -1, i -3, i -4, and i -s, which is the current through the power supply first.
05:50
So let's determine these currents.
05:56
First one we'll do, we'll just pick a loop, use our loop rule, and therefore the potential difference across r3 v3 is equal to 20 volts, and therefore 20 volts over 5 oms, i3, the current through resistor 3, must be 4 amps.
06:22
Alright, the next trick is i'm going to simplify this circuit a little bit, so i'm going to redraw it with an equivalent circuit.
06:30
That has my, just to make it a little easier for us.
06:36
So i'm still going to keep that 5 -em over there...