Average back emf induced in coil

[lloyd21]

Homework Statement

hey! I saw you've answered this question before...

Hi,
I would appreciate any help with the following:

The coil in a loudspeaker has an inductance of L = 112 microH. To produce a sound of frequency 40kHz, the current must oscillate between peak values of + and - 4.4 A in half a period. What average back emf is induced in the coil during this variation?

My main confusion is, why do we need to know the half period thing...I have no idea how to incorporate it into the solution.

Here's what I have now:

Xl = inductive reactance = 2 pi f L = 2 pi 40 x 10^3 x 112 x 10^-6 = 28.15 Ohm.

Then I rms = I/sqrt 2 = 4.4/sqrt 2 = 3.11 A. Am I correct in looking at rms values here?

Then V rms = I rms x Xl = 3.11 x 28.15 = 87.5 V.

Is that all? Is this V rms the average induced back emf they are asking for? Or am I wrong? I'm really confused about this one.

Any help would be much appreciate! Thanks!The back-emf created by an inductor depends upon the rate of change of the current flowing through it. Thus for an inductance L,
V=LdIdt
Iam stuck at the same part. With the v= dI / dt ...wouldn't that give the answer of 1 V?

Homework Equations

The Attempt at a Solution

 

[gneill]

I believe that they want you to consider a particular period of a cycle where the current will be changing monotonically. Otherwise the average value of the current or back emf (or any other sinusoidal signal) over an extended time is zero.

So sketch a cosine function. Pick the first half cycle where it goes from max value to min value. Hint: that's the very first half cycle for a cosine.

Do some calculus. You should be able to write the expression for the current function. Find the back emf function. Average the back emf over the chosen period.

 

[lloyd21]

It says there should not be any calculus involved?

 

[gneill]

It says there should not be any calculus involved?

I never saw that limitation. Then perhaps the question is badly phrased and "average" doesn't mean what it should in this context. It certainly is a confusing matter if they identify a particular portion of a cycle and ask for an average during that period and don't expect the use of calculus, and then it turns out they actually want something else entirely.

I suppose then they really just want the rms value of the voltage as the original poster laid out.

 

[Hesch]

I think that an emf(t) can be calculated as for a fixed coil ( windings glued and so on ), but mounted in a loud-speaker in a magnetic field, the coil and the attached membrane will oscillate when an ac-current is induced. That's the purpose. Thus the coil will cross the magnetic field and an unpredictable emf will be induced, because the movements depend on mass of the coil+membrane and sound pressure on the membrane, and we don't know the masses and the pressure.

 

[NascentOxygen]

The coil in a loudspeaker has an inductance of L = 112 microH. To produce a sound of frequency 40kHz, the current must oscillate between peak values of + and - 4.4 A in half a period. What average back emf is induced in the coil during this variation?

In a pure inductance, during the interval where instantaneous current swings from +A_max to -A_max the voltage waveform goes through one unipolar halfcycle. You should be able to determine the mean value of that voltage waveform during that half-period interval.

I think that's probably all that is intended.