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An LC resonant circuit contains a 400 pF capacitor and a 100 $\mu$H inductor. It is set into oscillation and coupled to an antenna. The wavelength of the radiated electromagnetic waves is

1. 377 mm
2. 377 metre
3. 377 cm
4. 3.77 cm

Correct answer: 377 metre

Solution

The resonant frequency of the LC circuit is $f = \frac{1}{2\pi\sqrt{LC}}$. With $L = 100\,\mu\text{H}$ and $C = 400\,\text{pF}$, this gives a frequency of about $7.96\times10^5$ Hz. The corresponding wavelength is $\lambda = c/f \approx 377$ m.

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