The problem is, "There are two 120 motors wired in series, one is 60 watts and one is 4 watts. The result is; "

A. Both motors operate normally. B. Neither motor operates normally. C. Only the 60 watt motor operates. D. Only the 4 watt motor operates.

I'm more interested in the math behind this problem. To try and figure this out I made the following calculations:

using P1 = (E^2)/R1 ----> R1 = E^2/P1 -----> R1 = (120^2)/60 = 240 ohms.

Then R2 = (120^2)/4 = 3600 ohms

I didn't use voltage drops in this calculation because I figured the motors were designed for these specs.

Next, I wanted to find the total amps on the circuit (now imagining them wired in series).

I used three different formulas from the power wheel.

IT = PT/ET ----> IT = 64/120 = .53333A

IT = sqrt(PT/RT) -----> IT = sqrt(64/3840) = 0.1289A.

IT = ET/RT ----> IT = 120/3840 = .03125A

I expected these values to be equal, but, they are not. I tested out all of these values trying to calculate the voltage drop across each resistor.

Voltage was conserved only when I used the third value.

E1 = 240(.03125) = 7.5V

E2 = 3600(.03125) = 112.5V

E1 + E2 = 120V

Then I calculated the amp draw for both motors.

I1 = sqrt(60/240) = 0.5A

I2 = sqrt(4/3600) = .033333A

My conclusion, based on these calculations, is that neither motor is operating normally because there aren't enough amps on the circuit (.03125A) to satisfy their needs.

My questions are:

Am I wrong? If so what have I not considered?

If I am correct, is my reasoning sound, or did I come to the correct conclusion through faulty reasoning? (which is just as bad as getting it wrong)

On the power wheel it seems as if there are only two equations, Watt's Law and Ohm's Law, and they are used as a system of equations. Is this why the other two formulas I used yielded different results? (EDIT: I think I made a mistake by assuming the motors were dissipating the power they were rated for. I re-calculated the watts produced at each load based on the total amp value that I moved forward with, and the total watts produced was 3.872W, not 64W.)

As you can tell, I have very little experience modeling these types of problems so please bare with me.

A. Both motors operate normally. B. Neither motor operates normally. C. Only the 60 watt motor operates. D. Only the 4 watt motor operates.

I'm more interested in the math behind this problem. To try and figure this out I made the following calculations:

using P1 = (E^2)/R1 ----> R1 = E^2/P1 -----> R1 = (120^2)/60 = 240 ohms.

Then R2 = (120^2)/4 = 3600 ohms

I didn't use voltage drops in this calculation because I figured the motors were designed for these specs.

Next, I wanted to find the total amps on the circuit (now imagining them wired in series).

I used three different formulas from the power wheel.

IT = PT/ET ----> IT = 64/120 = .53333A

IT = sqrt(PT/RT) -----> IT = sqrt(64/3840) = 0.1289A.

IT = ET/RT ----> IT = 120/3840 = .03125A

I expected these values to be equal, but, they are not. I tested out all of these values trying to calculate the voltage drop across each resistor.

Voltage was conserved only when I used the third value.

E1 = 240(.03125) = 7.5V

E2 = 3600(.03125) = 112.5V

E1 + E2 = 120V

Then I calculated the amp draw for both motors.

I1 = sqrt(60/240) = 0.5A

I2 = sqrt(4/3600) = .033333A

My conclusion, based on these calculations, is that neither motor is operating normally because there aren't enough amps on the circuit (.03125A) to satisfy their needs.

My questions are:

Am I wrong? If so what have I not considered?

If I am correct, is my reasoning sound, or did I come to the correct conclusion through faulty reasoning? (which is just as bad as getting it wrong)

On the power wheel it seems as if there are only two equations, Watt's Law and Ohm's Law, and they are used as a system of equations. Is this why the other two formulas I used yielded different results? (EDIT: I think I made a mistake by assuming the motors were dissipating the power they were rated for. I re-calculated the watts produced at each load based on the total amp value that I moved forward with, and the total watts produced was 3.872W, not 64W.)

As you can tell, I have very little experience modeling these types of problems so please bare with me.

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