(a) Find the minimum inductance of the tank circuit. (b) Find the maximum induct

Question

(a) Find the minimum inductance of the tank circuit.


(b) Find the maximum inductance of the tank circuit.

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 1.68 x10^-11 F and a variable inductance. The antenna is intended to broadcast radio signals ranging in frequency from 4 MHz to 8 MHz. (a) Find the minimum inductance of the tank circuit. (b) Find the maximum inductance of the tank circuit.

Explanation / Answer

As the inductance increases, resonant frequency decreases
and vise versa.

f = 4 * 10 ^ 6 Hz (minimum frequency)
? = 2 ? f rad
C = 1.68 * 10 ^ -11 F
?^2 = 1/ (L*C)
Solve for L:
L = 1 / (? ^ 2 * C)
= 9.430906507115204E-05 H
= 94.3 uH (maximum inductance)

f = 8 * 10 ^ 6 Hz (maximum frequency)
? = 2 ? f rad
?^2 = 1/ (L*C)
Solve for L:
L = 1 / (? ^ 2 * C)
= 2.35E-05 H
= 23.5 uH (minimum inductance)

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