Consider the circuit shown in (Figure 1). The batteries have...

Consider the circuit shown in (Figure 1). The batteries have emfs of ?1 = 9.0 V and ?2 = 12.0 V and the resistors have values of R1 = 23 ?, R2 = 64 ?, and R3 = 36 ?. Part C Determine the magnitudes of the currents in each resistor shown in the figure. Assume that each battery has internal resistance r = 1.0 ?. Express your answers using two significant figures separated by commas. I1, I2, I3 = Part D Determine the directions of the currents in each resistor. Assume that each battery has internal resistance r = 1.0 ?. I1 right, I2 left, I3 up I1 right, I2 left, I3 down I1 left, I2 right, I3 down I1 left, I2 right, I3 up

Transcript

00:01 Consider the circuit shown where even e2r or not 2 and r3 are given.

00:04 So we have to determine the magnitude of the current in each resistor, assuming that the battery has an internal resistance of, each battery has an internal resistance of 1 -on.

00:13 So that is not shown anywhere so make sure that we actually show this.

00:19 This is the 1 -oom.

00:20 And we have to find a direction of each of the current as well.

00:25 So that can be done.

00:28 Let's assume that the direction.

00:33 Of each current okay so let's assume that the current flowing through i r1 was i1 flowing through r2 was i2 and flowing through r3 was i3 and this is the point a or the node a so if you apply the kcel then incoming current i3 should be equal to the outgoing current that is the first equation then from a if we applied the uh the two loops are to be taken like this kvl so the upper loops equation is going to be e1, sorry, not even first, the internal resistance comes.

01:09 So minus i1 times the internal resistance r plus e1 minus i1r1 plus i2 r2 is equal to 0.

01:20 This means that internal resistance r is 1, so that's just negative i1.

01:25 E1 is 9.

01:28 R1 is 23 and r2 is 64.

01:34 This is equal to 0.

01:36 So this can be simplified as 9 minus 24 i1 plus 64 i2 is equal to 0.

01:44 So this is equation number 1.

01:47 This is equation number 2.

01:48 For equation number 3, we have negative i2 r2, negative i3.

02:00 3r3, then along the current that's going to be negative i3 smaller, then we have negative negative e2 that is actually equal to 0.

02:10 So there are all over the place we have the negative signs.

02:16 So we can just multiply by minus 1 to get rid of all the negatives.

02:20 What is r2? 64...

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