Question

The terminal voltage across a single phase of a stepper motor used as a generator is applied across a load resistor of 33 ohms. This terminal voltage has an amplitude of 18.7V and a frequency of 242 Hz. From a previous measurement, we know that this stepper motor phase has an internal resistance of 11.2 ohms. What is the time-averaged power delivered to the load? What is the electrical efficiency of this circuit? Write down an expression for the instantaneous (i.e. as a function of time) current flowing through the load.

Answer 1

Terminal Voltage = 18.7 V x cos ( 2pi f t) , where f = frequency of the AC supply)

This terminal voltage is driving current through total resistance (33+11.2)Ohms = 44.2 Ohms

Current in the circuit = (18.7/44.2) cos ( 2pi f t ) = 0.42 Cos ( 2 pi f t)

Potential across load = 18.7 x Cos(2pi f t) - (18.7/44.2)(11.2) cos(2pi f t) = 18.7(1-11.2/44.2) cos(2pi f t) =14 cos(2pi f t)

Potential across internal resistance = (18.7-14) cos(2pi f t) = 4.7 cos(2 pi f t)

Power delivered to load = 14 cos(2pi f t) x (18.7/44.2)cos(2pi f t) =5.92 cos^2(2pi f t)

<Pload> = 5.92 /2 = 2.96 Watts

Power delivered to internal resistance = (18.7/44.2) cos(2pift) x 4.7 cos(2pift)

=1.99 Watts

Average power delivered to Internal resistance =<Pr>=1.99 watts/2 =0.99 Watts

Power efficiency = Power delivered to load/( Total Power) = 2.96 Watts / (0.99+2.96)W

= 0.749 or 74.9%

Current flowing in the circuit = 0.42 Cos ( 2 pi f t) ( calculated in Earlier steps )