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 1.78 x 1011 F and a variable inductance. The antenna is intended to broadcast radio signals ranging in frequency from 8 MHz to 11 MHz. (a) Find the minimum inductance of the tank circuit. (b) Find the maximum inductance of the tank circuit.

Explanation / Answer

a) f = w / 2 pi

= 1 / 2 pi * sqrt [LC]

11 * 106 = 1 / 2 pi * sqrt [1.78 * 10-11 * L]

minimum inductance L = 1.18 * 10-5 H

b) f = w / 2 pi

= 1 / 2 pi * sqrt [LC]

8 * 106 = 1 / 2 pi * sqrt [1.78 * 10-11 * L]

maximum inductance L =2.22 * 10-5 H

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