Handbook for Sound Engineers

Grounding and Interfacing 1183

frequency since an increase in either causes an increase

in current, corresponding to a decrease in reactance.

(32-3)

where,
XC is capacitive reactance in ohms,
f is frequency in hertz,
C is capacitance in farads.

In general, capacitors behave as open circuits at dc
and gradually become short circuits, passing more and
more current, as frequency increases.
As shown in Figure 32-4, a magnetic field exists
around any conductor carrying current at right angles to
the axis of flow. The strength of the field is directly
proportional to current. The direction, or polarity, of the
magnetic field depends on the direction of current flow.
Inductance is the property that tends to oppose any
change in the strength or polarity of the field. Note that
the fields around the upper and lower conductors have
opposite polarity. The fields inside the loop point in the
same direction, concentrating the field and increasing
inductance. An electronic component called an inductor
(or choke) is most often made of a wire coil with many
turns to further increase inductance. Inductance is
denoted L in equations and its unit of measure is the
henry, abbreviated H. Again, remember that uninten-
tional or parasitic inductances are important, especially
in wires!

If we abruptly apply a dc voltage to an inductor, a

magnetic field is generated within the wire and moves

outward as current begins to flow. But, in accordance

with the law of induction, the rising field strength will

induce a voltage, called back emf, in the wire which

works to oppose current flow. The faster the field

increases its strength, the more back emf will be

induced to oppose current flow. The net result is to slow

the buildup of current as it approaches its final value,

which is limited by the applied voltage and circuit resis-

tance. In ac circuits, for a constant applied voltage, this

slowing reduces current flow as frequency increases

because less time is available each cycle for current to

rise. This apparent increase in ac resistance is called

inductive reactance. Inductive reactance increases in

direct proportion to both inductance and frequency.

(32-4)

where,

XL is inductive reactance in ohms,

f is frequency in hertz,

L is inductance in henrys.

In summary, inductors behave as short circuits at dc

and gradually become open circuits, passing less and

less current, as frequency increases.

Impedance is the combined effect of both resistance

and reactance for circuits that contain resistance, capaci-

tance, and inductance, which is the case with virtually

all real-world circuits. Impedance is represented by the

letter Z and is measured in ohms. Impedance can be

substituted for R in the Ohm’s Law equations. Imped-

ance is a more general term than either resistance or

reactance and, for ac circuits is the functional equivalent

of resistance.

32.2.4 Single Wires

The electrical properties of wire are often overlooked.

Consider a 10 ft length of #12 AWG solid copper wire.

1. The resistance of a wire is directly proportional to
   its length, inversely proportional to its diameter,
   and depends strongly on the material. From stan-
   dard wire tables, we find the dc resistance of
   #12 AWG annealed copper wire is 1.59:/1000 ft
   or 0.0159: for a 10 ft length. At frequencies
   below about 500 Hz, this resistance largely sets the
   impedance.


2. The inductance of a straight wire is nearly indepen-
   dent of its diameter but is directly proportional to
   its length. From the formula for the inductance of a
   straight round wire,^1 we find its inductance is
   4.8μH. As shown in Fig. 32-5, this causes a rise in
   impedance beginning at about 500 Hz, reaching
   30 : at 1 MHz (AM radio). Replacing the wire
   with a massive ½ inch diameter copper rod would
   reduce impedance only slightly to 23:.

Figure 32-4. Magnetic field surrounding conductor.

XC^1

2 SfC

-------------=

+

XL= 2 SfL