The coil in a loudspeaker has an inductance of L = 56uH (or 5.6 x 10^-5 H). To produce a sound frequency of 20 kHz, the current must oscillate between peak values of +2.2 A and -2.2 A in one half of a period. What average back emf is induced in the coil during this variation? How does this compare to the applied emf of 18V?
T = 1/f
emf = L(ΔI/Δt)
L = N(ΔΦB/Δl)
The Attempt at a Solution
back emf = (5.6 x 10^-5)[+2.2 - (-2.2)/Δt]
My problem here is I do not know where I can obtain Δt. I am assuming that it has something to do with the frequency of 20kHz in one half period (1/2T).
T = 1/f --> 1/2T = 1/f --> 2/f -- > T = 2/20000 = 1.0 x 10^-4 secs
If this is the case then, by subbing, Δt = 1.0 x 10^-4 secs, into the above equation, I get:
back emf = (5.6 x 10^-5)[+2.2 - (-2.2)/1.0 x 10^-4 secs]
= (5.6 x 10^-5)[4.4/1.0 x 10^-4 secs]
= (5.6 x 10^-5)(44000)
= 2.464 V
Is this correct?