# AP Physics C Montwood High School R. Casao

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AP Physics C Montwood High School R. Casao
Generators and Motors AP Physics C Montwood High School R. Casao

Generators and motors are important devices that operate on the principle of electromagnetic induction. Consider the alternating current (AC) generator, a device that converts mechanical energy to electrical energy. In simple form, the AC generator consists of a loop of wire rotated by some external means in a magnetic field.

In commercial power plants, the energy required to rotate the loop can be derived from a variety of sources: falling water directed onto turbine blades to produce rotary motion in a hydroelectric plant; heat produced by burning coal converts water to steam which is directed against turbine blades to produce rotary motion in a coal-fired plant. As the loop rotates, the magnetic flux thru the loop changes with time, inducing an EMF and a current in an external circuit. The ends of the loop are connected to slip rings that rotate with the loop. Connections to the external circuit are made by stationary brushes in contact with the slip rings.

Suppose that the AC generator loop has N turns, all of the same area A, and rotates with constant angular velocity ω. If  is the angle between the magnetic field B and the normal to the plane of the loop (the area vector A), then the magnetic flux thru the loop at any time t is: Φm = B·A·cos  = B·A·cos (ω·t), where  = ω·t and the clock is set so that t = 0 s when  = 0 rad. The induced EMF in the coil is:

The EMF varies sinusoidally with time.
The maximum EMF occurs when sin (ω·t) = 1 and has the value EMFmax = N·B·A·ω. This occurs when the angle  = ω·t between the magnetic field B and the area vector A is 90º and 270º.

EMF = EMFmax when the magnetic field is in the plane of the coil and the time rate of change of magnetic flux is a maximum. EMF = 0 V when the angle  = ω·t between the magnetic field B and the area vector A is 0º and 180º. This occurs when the magnetic field vector is perpendicular to the plane of the coil and the time rate of change of magnetic flux is zero.

EMF Induced in a Generator
The frequency (ω = 2·π·f) for commercial generators in the US and Canada is 60 Hz; some European countries use 50 Hz. EMF Induced in a Generator An AC generator consists of 8 turns of wire of area 0.09 m2 and total resistance 12 . The loop rotates in a magnetic field of 0.5 T at a constant frequency of 60 Hz. What is the maximum induced EMF?

What is the maximum induced current?
Determine the time variation of the induced EMF and the induced current when the output terminals are connected by a low- resistance conductor.

The direct current (DC) generator is used to charge storage batteries in older cars.
The components are essentially the same as those of the ac generator, except that the contacts to the rotating loop are made using a split ring, or commutator. The output voltage always has the same polarity and the current is a pulsating direct current.

The reason for the pulsating direct current occurs because the contacts to the split ring reverse their roles every half cycle. At the same time, the polarity of the induced EMF reverses; so the polarity of the split ring (which is the same as the polarity of the output voltage) remains the same. A pulsating DC current is not suitable for most applications. To obtain a more steady DC current, commercial DC generators use many armature coils and commutators distributed so that the sinusoidal pulses from the various coils are out of phase. When the pulses are superimposed, the DC output is almost free of fluctuations. Motors Motors are devices that convert electrical energy into mechanical energy.

A motor is a generator operating in reverse.
Instead of generating a current by rotating a loop, a current is supplied to the loop by a battery and the torque acting on the current-carrying loop causes it to rotate. Useful mechanical work can be done by attaching the rotating armature to some external device. As the loop rotates, the changing magnetic flux induces an EMF in the loop. The induced EMF always acts to reduce the current in the loop; if not, Lenz’s law would be violated. The back EMF increases in magnitude as the rotational speed of the armature increases. The back EMF is an EMF that tends to reduce the supplied current.

Since the voltage available to supply current equals the difference between the supply voltage and the back EMF, the current thru the armature coil is limited by the back EMF. When a motor is first turned on, there is initially no back EMF and the current is very large because it is limited only by the resistanc of the coil. As the coils begin to rotate, the induced back EMF opposes the applied voltage and the current in the coils is reduced. If the mechanical load increases, the motor will slow down, which causes the back EMF to decrease. The reduction in the back EMF increases the current in the coils and therefore increases the power needed from the external voltage source. For this reason, the power requirements are greater for starting a motor and for running it under heavy loads.

The Induced Current in a Motor
If the motor is allowed to run under no mechanical load, the back EMF reduces the current to a value just large enough to overcome losses due to heat and friction. If a very heavy load jams the motor so that it cannot rotate, the lack of a back EMF can lead to dangerously high current in the motor’s wires. The Induced Current in a Motor Assume that a motor having coils with a resistance of 10  is supplied by a voltage of 120 V. When the motor is running at its maximum speed, the back EMF is 70 V. Find the current in the coils when the motor is first turned on. When the motor is first turned on, the back EMF is 0 V.

The current in the coils is maximum and equal to:
Find the current in the coils when the motor has reached maximum speed. At the maximum speed, the back EMF has its maximum value. The effective supply voltage is now the external source minus the back EMF. The current is reduced to:

Suppose that the motor is in a circular saw
Suppose that the motor is in a circular saw. You are operating the saw and the blade becomes jammed in a piece of wood so that the motor cannot turn. By what percentage does the power input to the motor increase when it is jammed? The reason an object with a motor can become warm when the motor is prevented from turning is due to the increased power input to the motor. The higher rate of energy transfer results in an increase in the internal energy of the coil, which is undesirable. When the motor is jammed, the current is 12 A; when the motor is free to turn, the current is 5A.

Pjammed = 5.76·Pnot jammed; this represents a 476% increase in the input power.
The high power input when the motor is jammed can cause the coil to heat up to the point where it is permanently damaged.