Handbook for Sound Engineers

1182 Chapter 32

Although the resistance of wires that interconnect
circuit elements is generally assumed to be negligible,
we will discuss this later.
In a parallel circuit, the total source current is the
sum of the currents through each circuit element. The
highest current will flow in the lowest resistance,
according to Ohm’s Law. The equivalent single resis-
tance seen by the source is always lower than the lowest
resistance element and is calculated as

(32-1)

In a series circuit, the total source voltage is the sum
of the voltages across each circuit element. The highest
voltage will appear across the highest resistance,
according to Ohm’s Law. The equivalent single resis-
tance seen by the source is always higher than the
highest resistance element and is calculated as

(32-2)

Voltages or currents whose value (magnitude) and
direction (polarity) are steady over time are generally
referred to as dc. A battery is a good example of a dc
voltage source.

32.2.2 ac Circuits

A voltage or current that changes value and direction
over time is generally referred to as ac. Consider the
voltage at an ordinary 120 V, 60 Hz ac receptacle.
Since it varies over time according to a mathematical
sine function, it is called a sine wave. Figure 32-3 shows

how it would appear on an oscilloscope where time is

the horizontal scale and instantaneous voltage is the

vertical scale with zero in the center. The instantaneous

voltage swings between peak voltages of +170 V and

170 V. A cycle is a complete range of voltage or

current values that repeat themselves periodically (in

this case every 16.67 ms). Phase divides each cycle into

360 q and is used mainly to describe instantaneous rela-

tionships between two or more ac waveforms.

Frequency indicates how many cycles occur per second

of time. Frequency is usually denoted f in equations,

and its unit of measure is the hertz, abbreviated Hz.

Audio signals rarely consist of a single sine wave. Most

often they are complex waveforms consisting of many

simultaneous sine waves of various amplitudes and

frequencies in the 20 Hz to 20,000 Hz (20 kHz) range.

32.2.3 Capacitance, Inductance, and Impedance

An electrostatic field exists between any two conductors

having a voltage difference between them. Capacitance

is the property that tends to oppose any change in the

strength or charge of the field. In general, capacitance is

increased by larger conductor surface areas and smaller

spacing between them. Electronic components

expressly designed to have high capacitance are called

capacitors. Capacitance is denoted C in equations and

its unit of measure is the Farad, abbreviated F. It’s very

important to remember that unintentional or parasitic

capacitances exist virtually everywhere. As we will see,

these parasitic capacitances can be particularly signifi-

cant in cables and transformers!

Current must flow in a capacitor to change its

voltage. Higher current is required to change the voltage

rapidly and no current will flow if the voltage is held

constant. Since capacitors must be alternately charged

and discharged in ac circuits, they exhibit an apparent ac

resistance called capacitive reactance. Capacitive reac-

tance is inversely proportional to both capacitance and

Figure 32-1. The voltage is the same across all elements in
a parallel circuit.

Figure 32-2. The current is the same through all elements
in a series circuit.

+

Loads

Source Voltage

+

Source Current

Loads

REQ^1

1

R 1

------ -^1

R 2

------ -^1

R

--- }^1

n

++ +---

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

REQ=R 1 ++R 2 R 3 }+Rn

Figure 32-3. Sine wave as displayed on an oscilloscope.

0 o 90 o^180 o^270 o 360 o

One complete cycle

Volts

or

amps

+

Phase

Time

Peak

Peak