8.1 CURRENT AND VOLTAGE
In the manual ‘Fundamentals of
Electricity 1’ resistance in a circuit was likened to friction in a mechanical
system. It opposed any force attempting
to cause motion, and it absorbed energy which showed in the form of heat.
Unlike inductance which caused a
slow build-up of current, or unlike capacitance which caused a slow build-up of
charge, resistance has an instantaneous effect on the current in a circuit. In
a d.c. circuit Ohm’s Law states that:
where V is the d.c. voltage applied and / is the current (in amperes)
caused by that voltage. R is then
defined as the ‘resistance’ of the circuit and is measured in the unit ‘ohm’.
FIGURE 8.1
RESISTIVE CURRENTS, D.C.
AND A.C.
If Ohm’s Law is written in the form 
, the current (in amperes) in a d.c. circuit is equal to the
voltage divided by the resistance (in ohms) and starts to flow virtually
instantaneously the moment that the voltage is applied (see Figure
8.1(a)). For any given circuit or sample
the resistance is fixed (though it differs between samples), so that the
current too is constant and proportional to the voltage.
, the current (in amperes) in a d.c. circuit is equal to the
voltage divided by the resistance (in ohms) and starts to flow virtually
instantaneously the moment that the voltage is applied (see Figure
8.1(a)). For any given circuit or sample
the resistance is fixed (though it differs between samples), so that the
current too is constant and proportional to the voltage.
The same argument applies to a.c.
when it flows through a resistance.
Since at all times, and R is fixed, the current at any instant
is directly proportional to the voltage at that instant. As in an a.c. system the voltage is changing
periodically, so also will the current change periodically and will bear a
fixed ratio to the voltage at all times, as shown in Figure 8.1(b).
at all times, and R is fixed, the current at any instant
is directly proportional to the voltage at that instant. As in an a.c. system the voltage is changing
periodically, so also will the current change periodically and will bear a
fixed ratio to the voltage at all times, as shown in Figure 8.1(b).
Because of this fixed ratio the
current will reach its peaks at the same instants as the voltage, and it will
also pass through zero at the same instants as the voltage. This is shown clearly in Figure 8.1. The current is then said to be ‘in phase’
with the voltage.
It follows that Ohm’s Law applies
not only to d.c. but also to a.c. so long as the a.c. circuit consists only of
resistance, and in the a.c. case the resulting current is in phase with the
voltage.
The effect of inductance and
capacitance on the current in an a.c. circuit, and the consequent modification
of Ohm’s Law, is dealt with in Chapters 9 to 11.
8.2 HEATING
It was stated in the manual
‘Fundamentals of Electricity 1’ that, whenever a d.c. current is forced by
pressure of voltage to flow through a conductor which has resistance (and all
conductors do, even metals), heat is generated in that conductor. The rate of heat generation is proportional
to the resistance and to the square
of the current (in amperes squared).
That is to say, the heat generated is I2R, and,
since it represents a continuing loss of energy, it is expressed in the energy-rate
unit ‘watts’ (W).
FIGURE 8.2
CURRENT HEATING EFFECT
Consider now the heating effect of
an alternating current when flowing through a resistance R. In Figure 8.2(a) is a pure sine-wave current
trace with amplitude (or peak value) ‘A’.
In Figure 8.2(b) is the corresponding ‘current squared’ wave, whose amplitude
must be A2. Since the
square of a quantity, whether positive or negative, is always positive, the
current-
squared wave is wholly above the
line.
The rate of heat generation depends
on the resistance and the square of the current, so that the height of this
curve at any instant indicates the heating rate I2R at that
instant, and the area below the curve is the total heat generated over a given
period. The middle line (shown dotted)
is then the average rate of heat
generation. It therefore represents the
‘mean square’ current, and its height is ½A2.
It is shown in Chapter 5 that
currents in a.c. systems are measured not by their amplitudes or peak values
but by their ‘root mean square’ values, which were shown to be the square root
of the mean square current, or ‘root mean square’ (or ‘rms’ current for
short). This has
the value 
.
.
So long as the current measured (I) js the rms current (which it normally
is), then its square is the ‘mean square’ current which, when multiplied by R, determines the average heating
rate. Consequently with a.c. the average
heating rate is given by the expression I2R (where I is the rms current), which is the same expression as used for
d.c.
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