Handbook for Sound Engineers

1654 Chapter 48

where,

ejwt is cosAt + jsinAt or Euler’s identity.

Kirchhoff’s Current Law (KCL). Kirchhoff ’s current
law states that the sum of the branch currents leaving
any node must equal the sum of the branch currents
entering that node at any time.

Stated another way, the sum of all branch currents
incident at any node is zero.

In Fig. 48-2 the connection on node current in a dc
circuit is equal to 0 and is equal to the sum of currents
I 1 , I 2 , I 3 , I 4 , and I 5 or

(48-32)

or

(48-33)

The current throughout the circuit is also a function
of the current from the power source (V 1 ) and the
current through all of the branch circuits.

In an ac circuit, phase must be taken into consider-
ation, therefore, the current would be

(48-34)

where,

ejwt is cosAt + jsinAt or Euler’s identity.

Ohm’s Law. Ohm’s Law states that the ratio of applied

voltage to the resultant current is a constant at every

instant and that this ratio is defined to be the resistance.

If the voltage is expressed in volts and the current in

amperes, the resistance is expressed in ohms. In equa-

tion form it is

(48-35)

or

(48-36)

where,

e and i are instantaneous voltage and current,

V and I are constant voltage and current,

R is the resistance.

Through the use of Ohm’s Law, the relationship

between voltage, current, resistance or impedance, and

power can be calculated.

Power is the rate of doing work and can be expressed

in terms of potential difference between two points

(voltage) and the rate of flow required to transform the

potential energy from one point to the other (current). If

the voltage is in volts or J/C and the current is in

amperes or C/s, the product is joules per second or

watts:

(48-37)

or

(48-38)

where,

J is energy in joules,

C is electric charge in coulombs.

Fig. 48-3 is a wheel chart that relates current,

voltage, resistance or impedance, and power. The power

factor (PF) is cos I where I is the phase angle between e

and i. A power factor is required in ac circuits.

48.2 Radio Frequency Spectrum

The radio frequency spectrum of 30 Hz–

3,000,000 MHz (3 × 10^12 Hz) is divided into the various

bands shown in Table 48-2.

Figure 48-1. Kirchhoff’s voltage law.

Figure 48-2. Kirchhoff’s current law.

+

+

+

+ +

V 1

V 2

V 3

V 5 V 4

I 1 =I 2 +++I 3 I 4 I 5

I 1 – I 2 – I 3 – I 4 –0I 5 =

I 1

I 2

I 3

I 4

I 5

I 1 e

jZt

I 2 e

jZt

• I 3 e

jZt

• I 4 e

jZt

• I 5 e

jZt

–0=

R V

I

= ---

R e

i

= --

P=VI

J

s

--

J

C

--- -C

s

= ©¹§·--- -