In Example 6, what should be the capacitance in order to receive a 680-kHz radio signal?

Data from Example 6

In the antenna circuit of a radio, the inductance is 4.20 mH, and the capacitance is variable. What range of values of capacitance is necessary for the radio to receive the AM band of radio stations, with frequencies from 530 kHz to 1600 kHz? For proper tuning, the circuit should be in resonance, or X_L = X_C.  This means that

The capacitance should be capable of varying from 2.36 pF to 21.6 pF.

For fi 2nfL = 2nfC C = or C = C = = 530 kHz = 5.30 x 105 Hz and L = 4.20 mH 1 (2)(5.30 x 105)(4.20 10-) and for f = 1600 kHz = 1.60 x 106 Hz and L = 4.20 x 10-3 H, we have 1 (2)(1.60 x 106)(4.20 10-) (2f) L = = 4.20 x 10- H 2.15 x 10- F = 21.5 pF = 2.36 x 10-12 F = 2.36 pF