(3a) In the circuit below, V? and V? are two ideal...

(3a) In the circuit below, V? and V? are two ideal batteries. R?, R?, R?andR? are resistors. Calculate the value of the current through resistor R? for three cases: (14 points) (i) the switch S is open, (5 points) (ii) the switch S is in position '1' and (5 points) (iii) the switch S is in position '2'. V? = 30V, V? = 10V, R? = 1?, R? = 2?, R? = 3?andR? = 4?.(4 points)

Transcript

00:02 In this example, i'm going to be using kirkos laws to find the currents in a circuit.

00:08 Okay, so let me first show you the circuit we'll be working with.

00:13 Okay, so i have a circuit, simple circuit consisting of two power supplies.

00:17 I have a 12 volt here, 9 volt here, 3 resistors, sorry, 7 oms here, 8 oms here, 4 oms here, and i have a switch here.

00:28 We're going to be looking at the circuit in two different cases.

00:31 The first is how i have it drawn with our switch open.

00:35 And the second case will be with the switch closed here.

00:38 So as it's going to be closed, completing that circuit.

00:41 I'll start with the case of the switch, i mean the switch being open.

00:47 All right.

00:47 So we have no current flowing through this branch, the center branch of the circuit.

00:52 So for the first case with a switch open, i3 equals zero.

00:57 3 equals zero.

00:58 So we just need to find i1 and i2.

01:01 All right, let me redraw this circuit to make it a little simpler.

01:05 Right, so with the switch open, we get rid of the center branch and my circuit simply becomes our simplified circuit where we have two resistors and two batteries.

01:17 Notice the batteries are connected positive to positive so we can replace that with an equivalent battery of just three volts.

01:27 Right, so we have a three volt battery connected to two.

01:33 Resistors in series.

01:36 What do we know about equivalent resistance in series? we know it's simply the sum, rq, of the two resistors, equals r1, which is my 7 oms plus r2, which is my 8 oms.

01:47 That gives me an equivalent resistance of 15 oms.

01:52 All right.

01:53 I want to find the currents.

01:55 I know that i1 is going to equal i2.

01:57 That's i1, i2.

02:01 All right, because this is now, let me further.

02:04 To simplify the circuit we have three volts connected to across a 15 ome resistor all right so from oms law v equals i r we have i equals v over r which equals 3 over 15 volts oms equals 0 .2 ampers all right so for the switch being open our first case we have i1 equals i2 equals 0 .2 amps...

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