for each question please find vt total voltage it total current rttotal resistance v1 v2 v3 r1 r

1. For the first scenario, since the resistors are connected in series, the total resistance (Rt

For each question please find vt total voltage it total...

Series: Vt = V1 + V2 + V3 It = I1 = I2 = I3 Rt = R1 + R2 + R3 Parallel: Vt = V1 = V2 = V3 It = I1 + I2 + I3 1/Rt = 1/R1 + 1/R2 + 1/R3 1. Three resistors of 25Ω, 45Ω, and 75Ω are connected in series. A current of 2.0 A runs through the first resistor. 2. Three resistors of 25Ω, 45Ω, and 75Ω are connected in parallel. A current of 2.0 A runs through the first resistor. 3. Three resistors of 9Ω, 36Ω, and 18Ω are connected in series. A 189V battery is used.

Transcript

00:01 So in this problem, what we have is two different ways of connecting these two resistors are one in r2.

00:07 The first where they're in series and the second where they're in parallel.

00:11 So we're told that both of these circuits have the same total current running through them, but the total power differs.

00:17 So in the series circuit, we have the total power represented by ps.

00:21 And in the parallel circuit, we have the total power represented by pp.

00:26 So what we're going to do is we're going to begin to relate these elements to each other.

00:31 We can begin to find a value for the resistances.

00:35 So what we have here in this first circuit, if we want to relate the power to the current and the resistance, what we can do is we can use this formula here, where we have p for the power is equal to i squared, the current squared times the resistance.

00:52 So if we go ahead and apply this formula and to our series circuit here, what we'll find is that we take the equivalent resistance, which in this case is simply the sum of the resistances, since we're looking at a series circuit.

01:08 And we're going to equate that to ps, the total power, divided by i squared, the total current squared.

01:17 So we have an expression here that relates all of these elements together.

01:21 So we're going to go ahead and do the same thing with this second circuit, where these two resistors are in parallel.

01:27 So if we go ahead and find the equivalent resistance, that's going to look a little different.

01:36 Since we're looking at the two resistors in parallel, we're going to have r1 times r2 over r1 plus r2, since we're dealing with reciprocals in the case where we have two resistors in parallel.

01:51 And again, we're going to equate that to the total power divided by the current squared.

01:56 So what we're going to do now is we're going to go ahead and isolate r2 in this first equation that we set up...

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