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). or onerating

Answer 1

H Given, inductance of Coil, L= 2mH = 2810 Resonant Freequency, to 99.9 MHZ - 99.9 X106 HZ At resonant frequency inductive reactance become equal to Capacitive reactance : so, inderchive reactance e Copocitive reactance X = Xo who use (is the capacitance) > wa 1: W= afo) - 25 to a 14 h >> to a private => 99.9X10% = 2x3104/2x10*xc doxio xc = daxion XC = -527,382x106 > 2x10 x = ( 22.382106) 2x3.14% 99.9 xlo 6 9 RX 70'xc: 10-12 39 3 595.626 >> = 10-12 C 2 x 103 x 393595.626 ux 10-14393585628

> c= - 10-9 787191.252 - = 1.27x100x10-9 = 1.27 x 10-15 F Capacitance of Circuit should be 1.27810 Fareed So or