Question

1. Consider a radio receiver that is configured with a loop antenna, a variable capacitor and a pickup coil. By adjusting he value of the capacitance, it is possible to adjust the corresponding resonant frequency of the circuit and receive several radio stations. If the inductance of the coil is 2 mH, and we want to hear a radio station at 99.9 MHz, what is the capacitance of the circuit? (2 points).

Answer 1

given
L = 2 mH = 2*10^-3 H
f = 99.9 MHz = 99.9*10^6 Hz
C = ?

we know, f = 1/(2*pi*sqrt(L*C))

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

==> C = 1/(4*pi^2*L*f)

= 1/(4*pi^2*2*10^-3*99.9*10^6)

= 1.27*10^-7 F (or) 0.127 micro F <<<<<<<<--------------Answer