Building Services Engineering 5th Edition Handbook

Electrical installations 295
temperature would reveal a straight line of slope α.
R 40 = R 20 (1 + α × 20)
= 0.0069 × (1 + 0.00428 × 20)
= 0.0075
The relation between applied voltage, electric current and resistance is given by Ohm’s law:
I amps = V volts
R ohms
Figure 13.3 shows how an ammeter and a voltmeter are connected into a circuit to measure
power consumption. The load may be an electrical resistance heater or tungsten filament lamp,
in which case the power consumption in watts is found from:
power in watts = V volts × A amps × cos φ
for single-phase and,
power in watts = V volts × A amps × √ 3 × cos φ
for three-phase, where cos φ is the power factor (zero to unity). An electrical resistance heater
and tungsten lamps are purely resistive loads whose power factor, cos φ, is unity, 1.
Loads such as electric motors and fluorescent lamps have a property known as inductance,
which causes the current to lag behind the voltage that is producing that current. This is due to
an electromotive force (emf), that is, a voltage which opposes the incoming emf. The densely
packed electromagnetic windings of a motor have a high inductance and thus the 50 Hz cyclic
variation of voltage and current is opposed by the ‘inertia’ of the equipment. The opposing
emf comes from the expanding and collapsing magnetic fields of the input power around the
conductors.
The lag angle φ ◦ between peak voltage and peak current means that the instantaneous
available power is less than the product of the two peaks. Figure 13.4 shows voltage applied
across a circuit creating a current that lags in real time; peak current occurs after the peak
voltage.
Fuse
A
Ammeter
Alternating
current
supply
Voltmeter
V
Load
13.3 Measurements of power consumption in an electrical circuit.