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# The AM band extends from approximately 500 kHz to 1 600 kHz. If a 2.0-$\mu \mathrm { H }$ inductor is used in a tuning circuit for a radio, what are the extremes that a capacitor must reach to cover the complete band of frequencies?

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In this problem, the frequency of an AM band ranges from $f_\text{min} = 500~\mathrm{kHz} = 5.0 \times 10^{5}~\mathrm{Hz}$ to $f_\text{max} = 1600~\mathrm{kHz} = 1.6 \times 10^{6}~\mathrm{Hz}$. The inductor in the radio has inductance $L = 2.0~\mathrm{\mu H} = 2.0 \times 10^{-6}~\mathrm{H}$. We calculate the range of the capacitor to cover the frequency band.

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