Alternating current
Most students learning about electricity begin with what is known as direct current (DC),
which is electricity flowing in one direction only. DC is the kind of electricity made by a
battery, with definite positive and negative terminals.
However, we have seen that the electricity produced by some generators constantly
alternates (switches direction) and is therefore known as alternating current (AC). There are
a number of advantages to AC current, the main advantage to AC is that the voltage can be
changed using transformers. That means that the voltage can be "stepped up" at power
stations to a very high voltage so that electrical energy can be transmitted along power lines
at low current and therefore experience low energy loss due to heating. The voltage can
then be stepped down for use in buildings and street lights.
A list of the advantages of AC current:

Easy to be transformed (step up or step down using a transformer).

Easier to convert from AC to DC than from DC to AC.

Easier to generate.

It can be transmitted at high voltage and low current over long distances with less
energy lost.

High frequency used in AC makes it suitable for motors.
Interesting Fact:
In South Africa alternating current is generated at a frequency of 50 Hz.
The circuit symbol for alternating current is:
Current and voltage
In an ideal DC circuit, current and voltage are constant. In an AC circuit, current and voltage
vary with time. The value of the current or voltage at any specific time is called
the instantaneous current or voltage and is calculated as follows:
i is the instantaneous current. Imax is the maximum current. v is the instantaneous
voltage. Vmax is the maximum voltage. f is the frequency of the AC and t is the time at
which the instantaneous current or voltage is being calculated.
The value we use for AC is known as the root mean square (rms) average. This is the same
as what the DC voltage would be for the same source and is defined as:
Since AC varies sinusoidally, with as much positive as negative, doing a straight average
would get you zero for the average voltage. The rms value by-passes this problem.
Example 1: Laptop transformer
Question
The transformer for the laptop on which this book was written has the following information:

INPUT: 100-240 V; 1,5 A; 50/60 Hz

OUTPUT:20 V; 3,25 A
What changes from input to output, apart from the voltage and current values, and what
does that imply? In addition, calculate the rms (root mean square) current and voltage
values for the input and/or output as appropriate.
Answer
Comparing input and output
The input description includes a frequency because it is designed for regular household use
where we use alternating current. The output doesn't include a frequency. This implies that
the output is not alternating current. This means that the output voltage and current will be
constant with time.
RMS values
Root mean square values are only applicable when dealing with alternating current. The
transformer takes alternating current input and produces direct current output, this means
that we only need to determine the rms values for the input.
VrmsVrms=Vmax2√=240 V2√=169,71 V
Therefore Vrms=169,71 V
IrmsIrms=Imax2√=1,5 A2√=1,06 A
Therefore Irms=1,06 A
Example 2: Camera battery charger
Question
A camera charger has the following information:

INPUT: 100-240 V; 0,085 A (100 V) - 0,05 A (240 V) ; 50/60 Hz

OUTPUT:4,2 V; 0,7 A
Calculate the rms (root mean square) current and voltage values for both 100 V and 240 V
input.
Answer
Understanding the two cases
The reason the transformer has the different input voltages listed is because it may be used
internationally and not all countries use the same household voltage. The transformers
purpose is to ensure that the output is consistent regardless of the input voltage. The
different input voltages of 100 V and 240 V result in different input current values. This is
why two different current values are listed under input but the voltage in parentheses tells
you which case they are applicable to.
The cases are:

100 V: 0,085 A

240 V: 0,05 A
Input voltage of 100 V
VrmsVrms=Vmax2√=100 V2√=70,71 V
Therefore Vrms=70,71 V
IrmsIrms=Imax2√=0,085 A2√=0,06 A
Therefore Irms=0,06 A
Input voltage of 240 V
VrmsVrms=Vmax2√=240 V2√=169,71 V
Therefore Vrms=169,71 V
IrmsIrms=Imax2√=0,5 A2√=0,35 A
Therefore Irms=0,35 A
Exercise 1: Alternating current
Problem 1:
Explain the advantages of alternating current.
Practise more questions like this
Answer 1:

Easy to be transformed (step up or step down using a transformer).

Easier to convert from AC to DC than from DC to AC.

Easier to generate.

It can be transmitted at high voltage and low current over long distances with less
energy lost.

High frequency used in AC makes it suitable for motors.
Problem 2:
Which of the following graphs correctly shows the current vs. time graph for an AC
generator?
A
B
C
D
Table 1
Practise more questions like this
Answer 2:
For an alternating current generator, the current vs. time graph is a sine wave and
alternates between positive and negative values.
For a direct current generator, the current vs. time graph is the absolute value of a sine
wave and does not alternate between positive and negative values.
The correct answer is C.
Problem 3:
Write expressions for the current and voltage in an AC circuit.
Practise more questions like this
Answer 3:
iv=Imaxsin(2πft+φ)=Vmaxsin(2πft)
Problem 4:
Define the rms (root mean square) values for current and voltage for AC.
Practise more questions like this
Answer 4:
The root mean square is the value that we use for AC and is what it's DC equivalent would
be.
IrmsVrms=Imax2√=Vmax2√
Problem 5:
What is the frequency of the AC generated in South Africa?
Practise more questions like this
Answer 5:
In South Africa the frequency is 50 Hz
Problem 6:
If Vmax at a power station generator is 340 V AC, what is the mains supply (rms voltage) in
our household?
Practise more questions like this
Answer 6:
Vrms=Vmax2√=3402√=240,42 V
Problem 7:
Given: Imax is 10 A
Calculate the rms (root mean square) current to two decimal places.
Practise more questions like this
Answer 7:
Irms=Imax2√
Irms=10 A2√=7,07 A
Therefore Irms=7,07 A
7.07
Problem 8:
Given: Vmax is 266 V
Calculate the rms (root mean square) voltage to two decimal places.
Practise more questions like this
Answer 8:
Vrms=Vmax2√
Vrms=266 V2√=188,09 V
Therefore Vrms=188,09 V
188,09 V
Problem 9:
Draw a graph of voltage vs time and current vs time for an AC circuit.
Practise more questions like this
Answer 9:
The graph is the same for both voltage and for current:
Power
If the current and voltage are functions of time, so they are always changing, then so will the
power that is dissipated in any circuit element. In circuits which contain only ohmic resistors
the average power dissipated in any component can be calculated in terms of the rms
values.
You might ask why we don't need to use an rms value for power. In an AC circuit both the
current and voltage have the same sign so they are both either positive or negative. This
means that power, the product of the two is always positive. If power is always positive then
the average value won't be zero as in the case of current or voltage in AC circuits.
Example 3: Laptop transformer power
Question
The transformer for a laptop has the following information:

INPUT: 100-240 V; 1,5 A; 50/60 Hz

OUTPUT:20 V; 3,25 A
Using the input values and assuming 240 V, what is the average power dissipated in the
transformer?
Answer
RMS values
As calculated previously:
VrmsVrms=Vmax2√=240 V2√=169,71 V
Therefore Vrms=169,71 V
IrmsIrms=Imax2√=1,5 A2√=1,06 A
Therefore Irms=1,06 A
Average power
Pav=IrmsVrms=1,06 A⋅169,71 V=179,89 W
Example 4: Motors and generators [NSC 2011 Paper 1]
Question
Diesel-electric trains make use of electric motors as well as generators.
1. 11.1.
The table below compares a motor and a generator in terms of the type of energy
conversion and the underlying principle on which each operates. Complete the table by
writing down only the question number (11.1.1–11.1.4) in the ANSWER BOOK and
next to each number the answer.
TYPE OF ENERGY
PRINCIPLE OF
CONVERSION
OPERATION
11.1.1
11.1.3
11.1.2
11.1.4
Motor
Generator
Table 2
(4 marks)
2. 11.2.
The simplified diagram below represents an electric motor.
Give a reason why the section of the coil labelled BC in the above diagram does not
experience a magnetic force whilst the coil is in the position as shown.
(2 marks)
3. 11.3.
Graphs of the current and potential difference outputs of an AC generator are shown
below.
Calculate the average power output of this generator.
(6 marks)
[TOTAL: 12 marks]
Answer
1
1. Electrical (energy) to mechanical (kinetic) energy
2. Mechanical (kinetic) energy to electrical (energy)
3. Motor effect
4. Electromagnetic induction
(4 marks)
Question 2
BC (conductor) is parallel to the magnetic field.
OR
Open switch, no current
(2 marks)
Question 3
Option 1:
OR
Option 2:
Option 3:
Option 4:
(6 marks)
[TOTAL: 12 marks]