Page 464 - Physics Coursebook 2015 (A level)

Cambridge International A Level Physics
Describing alternating current
In developed countries, mains electricity is a supply
of alternating current (a.c.). The first mains electricity supplies were developed towards the end of the 19th century; at that time, a great number of different voltages and frequencies were used in different places. In some places, the supply was direct current (d.c.). Nowadays this has been standardised across much of the world, with standard voltages of 110 V or 230 V (or similar), and frequencies of 50 Hz or 60 Hz.
In this chapter we will look at some of the reasons why a.c. has been chosen as standard. First, however, we must take a close look at the nature of alternating currents.
Figure 29.1 Public electricity supplies made possible new forms of street lighting and advertising.
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Sinusoidal current
An alternating current can be represented by a graph such as that shown in Figure 29.2. This shows that the current varies cyclically. During half of the cycle, the current is positive, and in the other half it is negative. This means that the current flows alternately one way and then the other in the wires in which it is travelling. Whenever
you use a mains appliance, current flows backwards and forwards in the wires between you and the power station where it is being generated. At any instant in time, the current has a particular magnitude and direction given by the graph.
The graph has the same shape as the graphs used to represent simple harmonic motion (see Chapter 19), and it can be interpreted in the same way. The electrons in a wire carrying a.c. thus move back and forth with s.h.m. The current varies like a sine wave and so it is described as sinusoidal. (In principle, any current whose direction changes between positive and negative can be described as alternating, but we will only be concerned with those which have a regular, sinusoidal pattern.)
QUESTION
1 The following questions relate to the graph of Figure 29.2.
a What is the value of the current I when time t = 5 ms? In which direction is it flowing?
b At what time does the current next have the same value, but negative?
c What is the time T for one complete cycle?
d What is the frequency of the alternating
current?
An equation for a.c.
As well as drawing a graph, we can write an equation to represent alternating current. This equation tells us the value of the current I at any time t:
I = I0 sin ωt
where ω is the angular frequency of the supply measured in rad s−1 (radians per second). This is related to the frequency f in the same way as for s.h.m.:
ω = 2πf
and the frequency and period are related by:
f = T1
The quantity I0 is known as the peak value of the alternating current, found from the highest point on the graph. (It is the amplitude of the varying current.)
I/A 3 2 1 0 –1 –2 –3
Figure 29.2
current.
5
10
15
20 25 30
35
t/ms
A graph to represent a sinusoidal alternating