Determine the range of capacitance

[zeshkani_usa]

Homework Statement

FM radio stations use radio waves with frequencies from 88.0 to 108 MHz to broadcast their signals. Assuming that the inductance in an LC-tuned circuit has a value of 7.60 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. Let your answer to (a) be the smaller of the two values that define the limits of the range, and (b) be the larger of the two.

Homework Equations

f = 1/ ((2pi)sqrt(LC))

The Attempt at a Solution

i used the euqation above converted the MHz to Hz and tried to Solve first for the Low frequency 88 for C but its the wrong answer this is how it looks for C

C = (sqrt(1/f2pi))/(L)

 

[physics girl phd]

your equation:
C = (sqrt(1/f2pi))/(L) is wrong. You did some algebra errors... to get rid of the sqrt in your first equation, you need to square some things. I'd also do BOTH calculations (for high and low frequency)... just to be sure you get the low and range correct (if you are using a homework system that might ask for the high end and low end separately). High frequency actually corresponds with LOW capacitance -- the capacitor gets filled up and discharges more quickly... the system isn't as sluggish.

 

[zeshkani_usa]

C = 1/((f^2)(2pi^2)L)

 

[zeshkani_usa]

C = 1/((8.8e7)^2(2pi)2(7.60e-7))
C = 4.303e-12