Average Back EMF Induced in Coil in Loudspeaker

AI Thread Summary
The discussion centers on calculating the average back emf induced in a loudspeaker coil with an inductance of 112 microH and a frequency of 40kHz, where the current oscillates between ±4.4 A. The user calculates the inductive reactance (28.15 Ohm) and the rms current (3.11 A), questioning if the resulting rms voltage (87.5 V) represents the average induced back emf. A response clarifies that the back emf is determined by the rate of change of current, emphasizing the importance of the half-period information for accurate calculations. Understanding this relationship is crucial for correctly determining the average back emf in the coil.
equinox2012
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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!
 
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equinox2012 said:
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!

Hi equinox2012, Welcome to Physics Forums.

The back-emf created by an inductor depends upon the rate of change of the current flowing through it. Thus for an inductance L,
$$V = L \frac{dI}{dt}$$
That's why the information about the change in current over a particular period of time was given.
 
Thank you for the help! ;)
 

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