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Re: Solenoid




Hi all,

M. A Santos writes:

I'm making two solenoids whose inductance I
want to measure. The way I do it is connecting a
solenoid in series with a resistor and then feeding
this circuit with a pulse signal(i.e. 1-0, 1-0,etc.)......

The small one seems to give a neat decay curve with a time
constant of 2microsec. using a 100 Ohms resistor. Well that means
L=t*R =0.2 mH..Disregarding the increase on L due to the different
layers with increasing section, I expect a value of
muo(pemeabilty of vacuum=4*pi*e-7 Wb/A)
n (density of turns)
S (Section of the solenoid)

L=muo*n*S=muo*(300/11*1e+2)*(pi*1e-4)=8e-7 H !!

This is the first problem.Huge discrepancy, isn't it?

The self-inductance goes as n^2, not n, since each turn both produces
field and has voltage induced. Smythe's book, Static and Dynamic
Electricity gives a slightly better approximation for a long solenoid
whose winding is thin compared to the radius

L = pi mu a^2 n^2 [sqrt(s^2 + a^2) -a]

where a = radius of coil and s = length of coil. This is in cgs
units. The conversion factor is 9 x 10^11

The second is that I cannot get a clean decay curve with
the second solenoid. It is usual to see damped-like oscillations
but here indeed I get a more abrupt oscillations intead of the
smooth ones. And this with any freq.(50-2k Hz range scanned.
Although most measurments were taken around 1K;may high-freq.
effects already be important?)

The coil has a distributed capacitance as well as inductance and
resistance. Your pulse is exciting the effective RLC circuit thus
formed, hence the ringing. The self-resonant frequency may indeed be
as low as a few kHz.

Any Idea of how coul I get a smoother decay?
Should I try to get L via phase-differences between the
current through R and L,rather than measuring decay time?

A better alternative is to use sine excitation and measure both
current and voltage to compute reactance. For a middle-range of
frequencies the inductive component will dominate both the resistive
and capacitive components. When using a grounded function generator
with a grounded scope, you will need to put the series resistor on the
ground side of the coil and keep the resistance small enough that the
voltage across it is negligible. An AC bridge would be more accurate,
although more work to set up.

Hope this helps.