Handbook for Sound Engineers

266 Chapter 10

(10-29)

In parallel with fields opposing

(10-30)

In series with fields aiding

(10-31)

In series with fields opposing

(10-32)

where,
LT is the total inductance in henrys,
L 1 and L 2 are the inductances of the individual coils in
henrys,
M is the mutual inductance in henrys.

When two coils are inductively coupled to give
transformer action, the coupling coefficient is deter-
mined by

(10-33)

where,
K is the coupling coefficient,
M is the mutual inductance in henrys,
L 1 and L 2 are the inductances of the two coils in henrys.

An inductor in a circuit has a reactance of j 2 SfL:.
Mutual inductance in a circuit also has a reactance equal
to j 2 SfM:. The operator j denotes reactance. The
energy stored in an inductor can be determined by

(10-34)

where,
W is the energy in joules (watt-seconds),
L is the inductance in henrys,
I is the current in amperes.

Coil Inductance. The following is the relationship of
the turns in a coil to its inductance:

• The inductance is proportional to the square of the
  turns.
  
  
  • The inductance increases as the permeability of the
    core material is increased.
  
  
  • The inductance increases as the cross-sectional area
    of the core material is increased.
  
  
  • The inductance increases as the length of the winding
    is increased.
  
  
  • A shorted turn decreases the inductance. In an audio
    transformer, the frequency characteristic will be
    affected, and the insertion loss increased.
  
  
  • Inserting an iron core in a coil increases the induc-
    tance; hence, its inductive reactance is increased.
  
  
  • Introducing an air gap in an iron core coil reduces the
    inductance.
  
  
  
  

The maximum voltage induced in a conductor

moving in a magnetic field is proportional to the

number of magnetic lines of force cut by the conductor

moving in the field. A conductor moving parallel to the

lines of force cuts no lines of force so no current is

generated in the conductor. A conductor moving at right

angles to the lines of force will cut the maximum

number of lines per inch per second; therefore, the

voltage will be at the maximum.

A conductor moving at any angle to the lines of

force cuts a number of lines of force proportional to the

sine of the angles.

(10-35)

where,

V is the voltage produced,

E is the flux density,

L is the length of the conductor in centimeters,

v is the velocity in centimeters per second of the

conductor moving at an angle T.

The direction of the induced electromotive force

(emf ) is in the direction in which the axis of a

right-hand screw, when turned with the velocity vector,

moves through the smallest angle toward the flux

density vector. This is called the right-hand rule.

The magnetomotive force produced by a coil is

derived by

(10-36)

where,

T is the number of turns,

V is the voltage in volts,

R is the resistance of the wire in ohms,

LT^1

1

L 1 +M

----------------- M

L 2 +M

-----------------+

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

LT^1

1

L 1 – M

---------------- M

L 2 – M

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

LT=L 1 ++L 2 2 M

LT L 1 L 2 –+= 2 M

K M

L 1 uL 2

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

W LI

2

2

--------=

V=ELvsinTu 10 8–

ampere turns T V

R

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