Consider the circuit shown in Figure P18.9. (R = 31.0 ?...

Transcript

0:00 All right, hello.

00:01 In this question, we have two things we're trying to find.

00:03 We're asked, given this circuit, find the current in the 31 ohm resistor.

00:07 So there's going to be some current going through this that we want to find.

00:11 And we're also asked to find the voltage potential difference between points a and b.

00:16 So in order to do this, i'm going to simplify this circuit down a little bit.

00:21 So if i look at this, these two resistors here meet at this junction here.

00:27 And so from any other component, they're going to just look at one resistor.

00:32 And so they're going to have an equivalent resistance.

00:35 Since they're in parallel, it's going to be 1 over 10 plus 1 over 5 is equal to 1 over the equivalent resistance.

00:44 And then i know that my 5 ohm resistor and my 31 ohm resistor, they're going to have the same current going through them.

00:53 And from outside the circuit, from points a and b, they're going to look like a single resistor with a resistance of 36 ohms.

01:01 So i can go ahead and redraw this circuit a little bit.

01:04 And it'll look like this.

01:06 And now i have something that looks like this.

01:09 Well, if i follow from my positive terminal here and i go out, i'm going to hit this junction here.

01:15 And then the current's going to split that way and this way.

01:19 So i want to just redraw this again.

01:23 Well, so the current's going to go through those two resistors and then meet back up here and go through this resistor.

01:27 So i'm going to redraw this again just to make it a little more easy to understand.

01:34 So i'm going to have my voltage source.

01:36 And then i can either go through a 3 .33 ohm resistor or i can go through that 36 ohm resistor.

01:47 And then regardless, i'm going to meet back up and then go through a 10 ohm resistor before hitting the battery again.

01:55 And so i want to find the current in this 36 ohm resistor.

02:00 And the ab voltage points are going to be on either side of those two resistors.

02:05 So this circuit just looks a lot nicer and easier to understand.

02:10 So that's why i've done this.

02:12 And then in order to solve this even more, if this is 25 .10 volts, i'm going to redraw the circuit even simpler.

02:20 So i have 25 .0 volts here.

02:23 I'm going to go through one resistor and then through a second resistor, and then i'm back.

02:27 This will be my 10 ohm resistor...

Consider the circuit shown in Figure P18.9. (R = 31.0 ? .) (a) Find the current in the 31.0 ? resistor. (b) Find the potential difference between points a and b.