Handbook for Sound Engineers

270 Chapter 10

(10-64)

(10-65)

where,

Z is the impedance in ohms,

R is the resistance in ohms,

L is the inductance in henrys,

XL is the inductive reactance in ohms,

XC is the capacitive reactance in ohms.

T is the phase angle in degrees by which the current
leads the voltage in a capacitive circuit or lags the
voltage in an inductive circuit. 0° indicates an in-phase

condition.

10.5 Resonant Frequency

When an inductor and capacitor are connected in series
or parallel, they form a resonant circuit. The resonant
frequency can be determined from the equation

(10-66)

where,

L is the inductance in henrys,

C is the capacitance in farads,

XL and XC are the impedance in ohms.

The resonant frequency can also be determined

through the use of a reactance chart developed by the

Bell Telephone Laboratories, Fig. 10-28. This chart can

be used for solving problems of inductance, capaci-

tance, frequency, and impedance. If two of the values

are known, the third and fourth values may be found

with its use. As an example, what is the value of capaci-

tance and inductance required to resonate at a frequency

of 1000 Hz in a circuit having an impedance of 500:?

Entering the chart on the 1000 Hz vertical line and

following it to the 500: line (impedance is shown

along the left-hand margin), the value of inductance is

indicated by the diagonal line running upward as 0.08 H

(80 mH), and the capacitance indicated by the diagonal

line running downward at the right-hand margin is

0.3μF.

Z

R 1

2

XL

2

+ R 2

2

XC

2

+

R 1 +R 22 + XL–XC^2

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

Z atan

XLR 2

2

XC

2

+ XCR 1

2

XL

2

R 1 R 2

2

XC

2

+ R 2 R 1

2

XL

2

+ +

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

f^1

2 S LC

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

1

2 SCXC

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

XL

2 SL

----------=