1.
Electromagnetism
Topic 12.2 Alternating Current

2.
Rotating Coils
 Most of our electricity comes from huge
generators in power stations.
 There are smaller generators in cars and
on some bicycles.
 These generators, or dynamos, all use
electromagnetic induction.
 When turned, they induce an EMF
(voltage) which can make a current flow.

3.
 The next diagram shows a simple AC generator.
 It is providing the current for a small bulb.
 The coil is made of insulated copper wire and is
rotated by turning the shaft.
 The slip rings are fixed to the coil and rotate
with it.
 The brushes are two contacts which rub against
the slip rings and keep the coil connected to the
outside part of the circuit.
 They are usually made of carbon.

4.
AC Generator

5.
 When the coil is rotated, it cuts magnetic field
lines, so an EMF is generated.
 This makes a current flow.
 As the coil rotates, each side travels upwards,
downwards, upwards, downwards... and so on,
through the magnetic field.
 So the current flows backwards, forwards... and
so on.
 In other words, it is AC.

6.
 The graph shows how the current varies
through one cycle (rotation).
 It is a maximum when the coil is horizontal
and cutting field lines at the fastest rate.
 It is zero when the coil is vertical and
cutting no field lines.

7.
AC Generator Output

8.
The Sinusoidal Shape
 As the emf can be calculated from
ε = - N Δ (Φ/ Δt)
 and Φ = AB cos θ
 It can be clearly seen that the shape of the curve
must be sinusoidal.

9.
 The following all increase the maximum
EMF (and the current):
 increasing the number of turns on the coil
 increasing the area of the coil
 using a stronger magnet
 rotating the coil faster.
 (rotating the coil faster increases the
frequency too!)

10.
Alternating Current
 The graph shows the values of V and I
plotted against time
 Can you see that the graphs for both V
and I are sine curves?
 They both vary sinusoidally with time.
 Can you see that the p.d. and the current
rise and fall together?
 We say that V and I are in phase.

11.
 The time period T of an alternating p.d. or
current is the time for one complete cycle. This
is shown on the graph
 The frequency f of an alternating pd or current is
the number of cycles in one second.
 Thepeak values V0 and I0 of the alternating p.d.
and current are also shown on the graph

12.
Root Mean Square Values
 How do we measure the size of an
alternating p.d. (or current) when its value
changes from one instant to the next?
 We could use the peak value, but this
occurs only for a moment.
 What about the average value?
 This is zero over a complete cycle and so
is not very helpful!

13.
 In fact, we use the root‑ mean‑ square
(r.m.s.) value.
 This is also called the effective value.
 The r.m.s. value is chosen, because it is
the value which is equivalent to a steady
direct current.

14.
 You can investigate this using the
apparatus in the diagram
 Place two identical lamps side by side.
 Connect one lamp to a battery; the other
to an a.c. supply.
 The p.d. across each lamp must be
displayed on the screen of a double ‑beam
oscilloscope.

15.
 Adjust the a.c. supply, so that both lamps
are equally bright
 The graph shows a typical trace from the
oscilloscope We can use it to compare the
voltage across each lamp.

16.
 Since both lamps are equally bright, the d.c. and
a.c. supplies are transferring energy to the bulbs
at the same rate.
 Therefore, the d.c. voltage is equivalent to the
a.c. voltage.
 The d.c. voltage equals the r.m.s. value of the
a.c. voltage.
 Notice that the r.m.s. value is about 70% (1/ √2)
of the peak value.

17.
 In fact:

18.
Why √2
 Why The power dissipated in a lamp
varies as the p.d. across it, and the current
passing through it, alternate.
 Remember power,P = current,(I) x p.d.,
(V)
 Ifwe multiply the values of I and V at any
instant, we get the power at that moment
in time, as the graph shows

19.
 The power varies between I0V0 and zero.
 Therefore average power = I0V0 / 2
 Or P = (I0 / √ 2) x (V0 / √ 2)
 Or P = Irms x Vrms

20.
Root Mean Square Voltage

21.
Root Mean Square Current

22.
Calculations
 Use the rms values in the normal
equations}
 Vrms = Irms R
P = Irms Vrms
P = Irms2 R
P = Vrms2 / R

23.
Transformers
A transformer changes the value of an
alternating voltage.
 It consists of two coils, wound around a
soft‑iron core, as shown

24.
 Inthis transformer, when an input p.d. of 2
V is applied to the primary coil, the output
pd. of the secondary coil is 8V

25.
 http://www.allaboutcircuits.com/worksheets/tra
 Transformer simulation

26.
How does the transformer
work?
 An alternating current flows in the primary coil.
 This produces an alternating magnetic field in
the soft iron core.
 This means that the flux linkage of the
secondary coil is constantly changing and so an
alternating potential difference is induced across
it.
 A transformer cannot work on d.c.

27.
An Ideal Transformer
 This is 100% efficient
 Therefore the power in the primary is
equal to the power in the secondary
 Pp = Ps
 i.e. I p V p = Is V s

28.
Step-up Step-down
A step‑up transformer increases the a.c.
voltage, because the secondary coil has
more turns than the primary coil.
 In a step‑down transformer, the voltage is
reduced and the secondary coil has fewer
turns than the primary coil.

29.
The Equation

30.
 Note:
• In the transformer equations, the
voltages and currents that you use must
all be peak values or all r.m.s. values.
 Do not mix the two.
 Strictly, the equations apply only to an
ideal transformer, which is 100 % efficient.