A tank circuit in a radio transmitter is a series RCL circuit connected to an an
ID: 1552035 • Letter: A
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 4 MHz to 12 MHz.
(a) Find the minimum inductance of the tank circuit. ______H
(b) Find the maximum inductance of the tank circuit.______ H
Explanation / Answer
The resonant frequency "f" of a tank circuit is:
2**f = 1/sqrt(L*C)
(2**f)^2 = 1/(L*C)
L = 1/[ (2**f)^2 * C ]
At 4 MHz:
L = 1/[ (2**4*10^6)^2 * 1.99*10^-11 ] = 79.5*10^-6 H =79.5 H
This is the maximum inductance. The minimum inductance is needed at the maximum tuned frequency.
At 12MHz:
L = 1/[ (2**12*10^6)^2 * 1.9*10^-11 ] = 8.83*10^-6 H = 8.83 H
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