Countertorque and Power of an Electric Generator



Countertorque and Power of an Electric Generator

In the previous example we assumed that the generator was operating under a no load condition, that is, that no current was drawn from the generator by electrical devices attached to it. When an external load it placed across the generator, current flows through the coil and out of the generator. The presence of current in the coil causes the magnetic field to exert a torque on the coil (as was discussed previously). By Lenz’s law, this magnetic torque opposes the torque that turns the generator and so is referred to as a countertorque.

Example

Suppose that the resistance of the coil of the generator of the previous example is 10.0 (. A load of 50.0 ( is placed across the terminals of the generator. (For simplicity ignore the internal friction of the generator and assume a purely resistive load.) Assume that enough power is delivered to the generator to maintain an rms terminal voltage of 120 V.

a. How much current is drawn from the generator?

Since the total resistance of the circuit is 60.0 (, [pic]

b. What electric power is consumed by the circuit?

[pic]

c. What is the rms countertorque on the coil? Assume three significant figures for all data.

First find the amplitude of the countertorque: [pic]

The rms countertorque is then [pic]

d. What rms mechanical power must be delivered to the generator to maintain its terminal voltage?

[pic]

Note that the mechanical power delivered to the generator matches the power output of the generator. Energy is conserved. In reality would you expect the mechanical power that must be delivered to the generator to be greater or smaller than the power output? Why?

The Back Emf Generated by an Electric Motor

The heart of any electric motor is a shaft connected to a coil that is suspended in a magnetic field (usually the magnetic field of a permanent magnet built into the motor). When current passes through the coil, the magnetic field exerts a torque on the coil, causing it and the shaft to spin. The shaft extends out of the motor where it can be connected to machinery or some other device that does work. The spinning coil, however, acts as an electric generator, producing a back emf or counter emf E in the circuit the motor is connected to. If the motor is connected to a voltage V the current drawn by the motor is then

[pic]

where R is the resistance of the motor’s coil.

Example

An electric fan designed to operate off of 120 vac has a coil of 25 turns, cross-sectional area 0.30 m2 and resistance 100 (. The permanent magnet in the fan’s motor produces a magnetic field of 0.50 T. When operating normally the fan spins at 400 RPM.

a. What is the back emf of the fan while it is operating?

[pic]

b. What current is drawn by the fan when it is first switched on?

When the fan is first switched on, it is not turning so that the back emf is zero:

[pic]

c. What current is drawn by the fan while it is operating?

[pic]

Note that the fan draws much more current when it is first switched on than when it is operating normally. This is typical of most appliances, and explains why a circuit breaker on an overloaded circuit is more likely to trip when a device on that circuit is first switched on.

The current drawn by the fan while it is operating provides the power to balance the friction on the fan’s moving parts. (Which moving parts experience friction?)

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