Fundamentals of Alternating currents (AC)
LEARNING OBJECTIVES
To know what is meant by alternating current and
how it is generated.
To identify sinusoidal terminology and calculate the
parameters.
To demonstrate the understanding of phasor
diagrams
DEFINITION
An alternating current (ac) is a current that
repeatedly reverses its direction.
FREQUENCY OF MAINS ELECTRICITY
Frequency (f) is the number of cycles per second.
The unit of frequency is the hertz (Hz)
Mains electricity we received is an alternating
current with a frequency of 50 Hz too fast to
notice flickering.
1
1
1
T
0.020s
period
f 50 Hz
frequency
Other types of Periodic Waveforms
Representation of Sinusoidal waveform
+Vm
v(t)
-Vm
v(t) = Vm sin ωt
If the waveform is ahead in its evolution it is said to be
leading and the one behind is said to be lagging.
MAXIMUM / PEAK VALUE
The maximum value of an alternating current
waveform is the maximum value which is the same in
either direction.
AVERAGE / MEAN VALUE
The average value is the arithmetic sum of all the
values divided by the total no. of values used to
obtain the sum.
In a pure sine wave if the average value is calculated over the
full cycle, the average value would be equal to zero as the
positive and negative halves will cancel each other out. So the
average of an AC waveform is calculated or measured over a
half cycle only.
EFFECTIVE VALUE
Imagine a heater (Resistance R) connected to an ac
supply.
It would repeatedly heat up then cool down.
The power, P, supplied to a heater of resistance R:
PI R
2
When I is at its maximum (Im ),
maximum power is
supplied.
When I is zero, zero power is supplied.
The mean power supplied:-
Pmean 2 I m R
1
2
ROOT MEAN SQUARE VALUE
The root mean square value or effective value of an
alternating current is the value of direct current that
would give the same heating effect as the alternating
current in the same resistor.
P I rms R
2
I rms R 2 I m R
2
I rms 2 I m
2
2
1
1
2
Im
I rms
2
Vm
Vrms
2
EXERCISE 1
What is the rms voltage of an ac mains with a
peak voltage of 325 V?
What would be the power supplied to a 70 ohm
resistor?
0
