Energy in electromagnetic waves question?

Question

what capacitance in needed in series with an 800 UH inductor to form a circuit that radiates a wavelength of 196 m?

Answer 1

The resonance condition is

ω = 1 / sqrt ( LC )

L = 800 x 10^-6 H

C = unknown

ω = f / 2π and λ = c / f, so using the given wavelength you can find the angular frequency ω and thus the required capacitance C.

Answer 2

λf = c = 3*10⁸m/s

f = 3*10⁸ / 196 m = 1.53 MHz

f = 1/(2π√LC)

1.53 MHz = 1/(2π√(0.8mH*C))

√(0.8mH*C) = 1/2π*1.53M = 10^-6 / 9.613

0.8mH*C = (10^-6 / 9.613)² = 0.01082e-12 = 1.082e-14

C = 1.082e-14 / 8e-4 = 0.1353e-10 or 13.5 pF

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