12.2 Alternating Current

12.2.1 Describe the emf induced in a coil rotating within a uniform magnetic field.

As the handle is turned, AB moves up through the field. As it cuts the field a current will be induced. Using Fleming's right hand rule --> direction of current is from A to B. Direction of motion of the right hand side (CD) is opposite so current is opposite. Result is a clockwise current through the resistor.


After turning half a revolution, side CD will now be moving up the field. Because of the slip rings, even though the current is still clockwise in the coil, it is anticlockwise in the resistor circuit.

12.2.2 Explain the operation of a basic alternating current (ac) generator.

A coil of wire rotates in the magnetic field due to an external force. As it rotates, the flux linkage of the coil changes with time and induces and e.m.f (refer to Faraday's law) causing current to flow.

Sides AB + CD will experience a force opposing the motion. (refer to Lenz's Law)

The work done rotating the coil generates electrical energy.

12.2.3 Describe the effect on the induced emf of changing the generator frequency.
If the speed of rotation is changed it will affect:


* Time period (distance between peaks)
* EMF (amplitude of peaks)


For example, if the speed is doubled therefore, the time period will be halved and the EMF (amplitude) will be doubled.

12.2.4 Discuss what is meant by the root mean squared (rms) value of an alternating current or voltage.

When the output of an a.c. generator is connected to a resistor, an alternating current will flow. A sinusoidal potential difference means a sinusoidal current. The graph shows that the average power dissipation is half the peak power dissipation for a sinusoidal current.

Thus the effective current through the resistor is (mean value of I^2)^0.5 and it is called the root mean square (rms) current. It is also know as the rating.


12.2.5 State the relation between peak and rms values for sinusoidal currents and voltages.

Mean value:



The rms value is the squareroot of this...

The current passing through the resistor will be proportional to the potential difference across it, so this will be sinusoidal, if the peak current is Io, the rms value will therefore be given by:

Questions
42. rms V =110 V
Vrms x V2 = 156 V


43. 4kW = 4000W , 220 V
P= VI, therefore I = P / V
I = 4000 / 220 = 18 A (to 2.s.f)


44. a) i) Calculating the angular velocity:

w= 2π x 50 = 100π rad s-1

ii) Calculating the maximum induced emf

BANw= Emax

100π x 500 x 5 x 10^-4 x 50 x 10^-3

= 3.9 V

iii) Calculating the rms emf 

= 2.8 V

b) Calculating the new Erms if the speed is reduced to 25 revolutions per second

Eo = 1.95 V

Erms= 1.95 / (2)^0.5 = 1.4 V

45. Calculate the resistance of a 1000 W bulb designed to operate at 220 V.


P = V^2 / R
R = V^2 / P
= 220^2 / 1000 = 48.4 ohms