Building Design and Construction Handbook - Merritt - Ventech!

15.10 SECTION FIFTEEN
E R and I R are in phase. In a circuit with impedance, however, the total circuit voltage
E Z is out of phase with the current by the phase angle �. In a series circuit, the
current I is in phase with E R; the voltage E Z, on the other hand, is out of phase
with E R by the angle �. In parallel circuits, the voltage E is in phase with E R,but
the current I Z is out of phase with E R. In both circuits, the power P is given by
P � EI (15.21)
R R
In series circuits, E r � E cos � and P � (E cos �)I R. In parallel circuits, I R � I
cos � and P � EI cos �. In any circuit with impedance angle �, therefore, the power
is given by
P � EI cos � (15.22)
Power Factor. The term cos � in Eq. (15.22) is called the power factor of the
circuit. Because it is always less than 1, it is usually expressed as a percentage.
Low power factor results in high current, which requires high fuse, switch, and
circuit-breaker ratings and larger wiring. Induction motors and certain electricdischarge-lamp
ballasts are a common cause of low power factor. Since they are
both inductive reactances (coils), the low power factor can be corrected by inserting
capacitive reactances in the circuit to balance the inductive effects. This can be
done with capacitors that are available commercially in standard kilovolt-ampere,
kVA, capacities.
For example, a 120-V, 600-kVA circuit with a 50% power factor has a current
of 5000 A. The actual power expended is only 300 kW, but the wire, switches, and
circuit breakers must be sized for 5000 A. If a capacitor with a 300-kVA rating is
wired into the circuit, the current is reduced to 2500 A, and the wiring, switches,
and circuit breakers may be sized accordingly.
Conversion of AC to DC. Alternating current has the advantage of being convertible
to high voltages by transformers. High voltages are desired for longdistance
transmission. For these reasons, utilities produce and sell alternating
current. However, many applications requiring accurate speed control need
direct-current motors, for example, building elevators and railroad motors, including
subways. In buildings, ac may be converted to dc by use of an ac motor to drive
a dc generator, which, in turn, provides the power for a dc motor. The ac motor
and dc generator are called a motor-generator set.
Another device used to convert ac to dc is a rectifier. This device allows current
to flow in one direction but cuts off the sine wave in the opposite direction. The
current obtained from the motor-generator set described previously is a similar
unidirectional current of varying instantaneous value. The only truly nonvarying
direct current is obtained from batteries. However, output filters can be added to
rectifiers to reduce the amount of voltage variation to nearly zero. In most cases
this is acceptable, and using a rectifier as a dc source eliminates the weight, cost,
and hazards involved with large storage batteries.
Single-Phase and Multi-Phase Systems. A single-phase ac circuit requires two
wires, just like a dc circuit. One wire is the live wire, and the other is the neutral,
so called because it is usually grounded (Fig. 15.3a).
A voltage commonly used in the United States is 240 V, single-phase, two-wire,
which is obtained from the two terminals of the secondary coil of transformers fed
from utility high-voltage lines. If a third wire is connected to the midpoint of the