Question

A radio can be tuned into a particular station frequency by adjusting the capacitance in an L-C circuit. Suppose that the minimum capacitance of a variable capacitor in a radio is 4.19 pFpF .

a. What is the inductance LLL of a coil connected to this capacitor if the oscillation frequency of the L-C circuit is 1.58 MHzMHz , corresponding to one end of the AM radio broadcast band, when the capacitor is set to its minimum capacitance?

b. The frequency at the other end of the broadcast band is 0.541 MHzMHz . What is the maximum capacitance CmaxCmaxC_max of the capacitor if the oscillation frequency is adjustable over the range of the broadcast band?

Answer 1

A. In LC circuit frequency is given by

XL = XC

wL = 1/wC

w = 2*pi*f

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

when f = 1.58 MHz = 1.58*10^6 Hz

C = 4.19 pF = 4.19*10^-12 F

then inductance, L = ?

L = 1/(4*pi^2*f^2*C)

L = 1/[(4*3.14^2*(1.58*10^6)^2*4.19*10^-12]

L = 2.42*10^-3 H = 2.42 mH = Inductance of coil

B.

for maximum capacitance:

Now on the other end, frequency = 0.541 MHz = 0.541*10^6 Hz

L = 2.42*10^-3 H

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

C = 1/[(2*3.14*0.541*10^6)^2*2.42*10^-3]

C = 35.8*10^-12 F = 35.8 pF

Let me know if you've any query.