Question

To receive AM radio, you want an RLC circuit that can be made to resonate at any frequency between 500 and 1650 kHz. This is accomplished with a fixed 9.94 µH inductor connected to a variable capacitor. What range of capacitance (in nF) is needed?

smallest value ________ nF

largest value _________ nF

Answer 1

here,

the inductance , L = 9.94 uH = 9.94 * 10^-6 H

the smallest frequency , f1 = 500 KHz = 500 * 10^3 Hz

let the capacitance for this frequency be C1

f1 = 1/2pi * 1/sqrt(L * C1)

500 * 10^3 = 1/2pi * 1/sqrt(9.94 * 10^-6 * C1)

solving for C1

C1 = 9.92 * 10^-7 F = 992 nF

the largest frequency , f2 = 1650 KHz = 1650 * 10^3 Hz

let the capacitance for this frequency be C2

f2 = 1/2pi * 1/sqrt(L * C2)

1650 * 10^3 = 1/2pi * 1/sqrt(9.94 * 10^-6 * C2)

solving for C2

C2 = 9.12 * 10^-8 F = 91.2 nF

the smallest value of capacitance is 91.2 nF

the largest value of capacitance is 992 nF