1250
F 14
Lecture 5-3
Assessment Problem
Why is inductance, L, proportional to the number of turns squared in an inductor?
ANS:
The voltage across each turn, vturn, is the same and is proportional to the
change in the magnetic flux, , through that turn:
vturn =
dL
dt
(1)
The turns are in series, so the total voltage drop, v, across the inductor is
the number of turns, N, times the voltage per turn, vturn:
v = Nvturn = N
dL
dt
(2)
The turns are close together, so the magnetic flux created by each turn,
turn, is felt by all the turns, and the total flux, , is N times the flux
created by one turn:
L = NLturn
(3)
Substituting for  in (2) gives a formula in which N2 appears:
v=N
dL
dNLturn
dL
=N
= N 2 turn
dt
dt
dt
(4)
Finally, we note that the flux created by one turn is proportional to the
current, i, in that turn:
Lturn = ki
(5)
where k is a constant.
(5) into (4) yields
v = kN 2
di
dt
(2)
From (6), we identify the inductance, L, as follows (since v = Ldi/dt):
L = kN 2
Thus, L is proportional to N2.
(2)