Help me out with thi question please! Consider the following RLC circuit, which

Question

Help me out with thi question please!

Consider the following RLC circuit, which we'll use as a model for a radio. Radio waves with different frequencies, f, hit the antenna and exert oscillating electric forces on the electrons in the antenna. Thus they act, via the antenna, as individual batteries, each oscillating at their particular frequency f. Suppose that R = 1200Ohm, then what should L and C be so that we get the largest current in the circuit at frequency f = 89.9 MHz, but at the frequency f= 90.3 MHz, the current is only 1110 as large (this will insure that we get a good reception)?

Explanation / Answer

largest current when at resonance frequency

so 2*pi*89.9E6 = 1/sqrt( L C)

L = 1/( 4*pi^2*89.9E6^2*C)

at 90.3E6 Hz we
want Z/R = 10

sqrt( 1200^2 + ( 2*pi*90.3E6*L - 1/(2*pi*90.3E6*C))^2) = 1200*10
plug in for L

sqrt( 1200^2 + ( 2*pi*90.3E6*1/( 4*pi^2*89.9E6^2*C) - 1/(2*pi*90.3E6*C))^2) = 1200*10

solve for C
C=1.32E-15 F

so L =
1/( 4*pi^2*89.9E6^2*1.32E-15)=2.37E-3 H

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