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ONLY NEED PART B SOLVED! THE CORRECT ANSWER TO PART A IS 1.23 microhenries. The

ID: 2030583 • Letter: O

Question

ONLY NEED PART B SOLVED!

THE CORRECT ANSWER TO PART A IS 1.23 microhenries.

The lowest frequency in the FM radio band is 88.0 MHz.

A) In order to construct an AC circuit that resonates at this frequency, what inductance, in microhenries, should be combined with a 2.65 pF capacitor? (CORRECT ANSWER IS 1.23)

B) The capacitor is variable, to allow the resonant frequency to be set as high as 108 MHz. With the inductance you found in part A, what must the capacitance be, in picofarads, to achieve this frequency?

Explanation / Answer

We know that resonance frequency is given by, when

XL = XC

w*L = 1/(w*C)

w = 2*pi*f

where f = resonance frequency

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

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

Using given values:

C = 1/(4*pi^2*(108*10^6)^2*1.23*10^-6)

C = 1.76*10^-12 F

C = 1.76 pF