Question

FM radio stations use radio waves with frequencies from 88.0 to 108 MHz to broadcast their signals. Assuming that the inductance has a value of 4.60 x 10^-7 H, determine the range of capacitance values that are needed so the antenna can pick up all the radio waves broadcasted by FM stations.

_____F (lowest acceptable capacitance)

____F (highest acceptable capacitance)


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Physics please help! - bobpursley, Wednesday, October 17, 2007 at 3:07pm
Find Xl (2PI f L)
then find C such that
Xc= 1/2PI*f*C where Xc= Xl

do it at each frequency end.

Please tell me where i went wrong.


Xl =(2*pi*f*L)
Xl = 2*3.142*(88.0x10^6)(4.60x10^-7)
Xl = 254.37632

I substitute this into the formula Xc= 1/2PI*f*C to find the value of C.

Xc = 1 / (2*3.1428(88.0x10^6)C)
254.37632 = 1 / 552992000 C
C = 7.11 x10^-12
According to the system this answer is incorrect for the lowest acceptable capacitance. Please tell me where I went wrong!

Answer 1

Do it for the other frequency (108Mhz). As frequency goes up, reactance goes down, so the lower cap is at the higher freq.