- #1

- 205

- 3

## Homework Statement

An electric motor connected to a 120 V, 60 Hz supply does work at a rate of 0.1 hp (1 hp = 746 W). If it consumes an rms (root mean square) current of 650 mA, what is its resistance, in terms of power transmission? Would this result be the same thing as the resistance of its coils, measured by an ohmmeter, with the motor disconnected from the generator?

## Homework Equations

## The Attempt at a Solution

The average power delivered by the power supply to the motor is [itex]P_{av} = i_{rms}^2R[/itex]. Since [itex]P=(0.1)(746)=74.6\ \mathrm{W}[/itex], and [itex]i_{rms} = 0.65\ \mathrm{A}[/itex], then [itex]R = \frac{74.6}{0.65^2} = 176.6\ \Omega[/itex] (this is the correct value at the back of the book).

My doubt regards the second question. I imagine that, since the resistance R that is used in the power formula of an RLC circuit is simply the resistance of the circuit, the value of the resistance should remain the same, even if it was measured by an ohmmeter with the motor stopped (it's just the impedance that would be different). However, the answer to this says that: "This would not be the same as the direct current resistance of the coils of a stopped motor, because there would be no inductive effects.".

Is my reasoning correct?

Thank you in advance.