2.1 INDUCTIVE CASE
In Chapter 1 it was shown that the true power
transmitted where the load is purely resistive is given by:
P
= VI watts
where V and I
are the rms values of voltage and current.
Consider now the purely inductive case, where there is
no resistance, as represented by Figure 2.1.
FIGURE 2.1
A.C. POWER - PURE INDUCTIVE LOAD
It has already been shown in the manual ‘Fundamentals of
Electricity 2’, Chapter 9, that, if the top wave represents the alternating
voltage, the second wave represents the current, which now lags one-quarter of
a cycle, or 90°, behind the voltage.
Using the same method as in Chapter
1, multiply the voltage and current at each instant. We now have:
At points A, B, C, D and E either the voltage or the current is zero, so that their product at all these points is zero.
FIGURE 2.2
A.C. POWER - PURE
CAPACITIVE LOAD
If the product (power) curve is now drawn, it will be as
the third wave of Figure 2.1. It will
be, as before, of double frequency but now it is symmetrical about the zero
line, and therefore the average power will be zero. Power is put in at each positive part and
taken out again at each negative part, giving a net power transmission of NIL.
2.2 CAPACITIVE CASE
It has been shown above that a current lagging 90° on the voltage, in the purely inductive case, gives rise to a
double-frequency power wave which is symmetrical about the axis and therefore
has no net or average power.
The purely capacitive case is quite similar except that
the current wave leads the voltage by 90°, as shown in Figure 2.2.
Exactly the same treatment as that given in para. 2.1
will produce the power wave at the bottom of Figure 2.2. Compared with that of Figure 2.1 it will be
reversed in sign, but it will still be symmetrical about the axis and therefore
will have no net or average power.
2.3 THE ‘VAR’ UNIT
The conclusions of both paras. 2.1
and 2.2 - namely that no net power is passed in either a purely inductive or
purely capacitive circuit - lead to a certain re-thinking of the power rules if
we are used only to d.c. If the d.c.
voltmeter reading is multiplied by the d.c. ammeter reading, the result is the
d.c. power in watts. In the a.c. case
however this is only true if the load is purely resistive (as in Chapter 1),
which it seldom is.
In the reactive cases (inductive or
capacitive) the voltmeter and ammeter readings can still be multiplied together,
but they do not now represent true power in watts. Yet the product is a perfectly good
figure. What then is it? It represents a ‘false power’ (the Germans
call it ‘blind power’) and it is measured in a unit called the ‘var’ (short for
volt-ampere-reactive). It is called
‘reactive power’, or sometimes ‘wattless power’ with symbol ‘Q’, and is
a measure of the energy stored (but not consumed) in a magnetised system. Since a platform or shore installation
consists of a vast number of transformers, motors, etc. which all need to be
magnetised, the demand for vars is considerable, as will be shown by the
varmeter (also a dynamometer instrument) now installed on most switchboards.
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