phy1020.DVI

so the inductance of a solenoid is

LD 0 n^2 A`D 0 N^2

A

`

: (37.7)

Note that the inductance, like the capacitance, depends only on factors involving the geometry of the inductor:
its length`, cross-sectional areaA, and number of turns of wireN.

37.2 Inductors in Series and Parallel

Inductors connected in series and parallel follow the same equations as resistors.
Several inductors connected end-to-end (in series) have an equivalent inductance equal to the sum of the
individual inductances:

LsD

X

i

Li (37.8)

DL 1 CL 2 CL 3 C (37.9)

If they are connectedin parallel, the the equivalent inductance is the reciprocal of the sum of the reciprocals
of the individual inductances:

1

Lp

D

X

i

1

Li

(37.10)

D

1

L 1

C

1

L 2

C

1

L 3

C (37.11)

Note the following points. For inductors connectedin series:

• The equivalent inductance will be bigger than the largest inductance in the series combination.


• If one inductor in the series combination is much larger than the others, the equivalent inductance will
  be approximately equal to the largest inductance.


• Mequal inductorsLconnected in series have an equivalent inductance ofML.

For inductors connectedin parallel:

• The equivalent inductance will be smaller than the smallest inductance in the parallel combination.


• If one inductor in the parallel combination is much smaller than the others, the equivalent inductance
  will be approximately equal to the smallest inductance.


• Mequal inductorsLconnected in parallel have an equivalent inductance ofL=M.

37.3 Magnetic Materials in Inductors

As shown by Eq. (37.7), the inductance of a solenoid can be increased by increasing the cross-sectional area
of the plates, or by increasing the number of turns of wire. Another way to increase the inductance is to insert
a magnetic material inside the solenoid; this will cause the inductance to increase by a factor ofKm:

LDKm 0 N^2

A

`

; (37.12)