A tank circuit in a radio transmitter is a series RCL circuit connected to an an

Question

A tank circuit in a radio transmitter is a series RCL circuit connected to an antenna. The antenna broadcasts radio signals at the resonant frequency of the tank circuit. Suppose that a certain tank circuit in a shortwave radio transmitter has a fixed capacitance of 1.99 10-11 F and a variable inductance. The antenna is intended to broadcast radio signals ranging in frequency from 8 MHz to 9 MHz.

(a) Find the minimum inductance of the tank circuit

in H

(b) Find the maximum inductance of the tank circuit

in H

Explanation / Answer

omega = 1/sqroot(C*L)

f = /2

so f = 1/ sqrt(CL)*2

a) minimum inductance when f is maximum.

so 1/9*10^6 = sqrt(CL)2

so L = 1.57*10^-5 H

b) maximum

1/8*10^6 = sqrt(CL)*2

so L= 1.99*10^-5 H

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