What should be the capacitance of the capacitor so that, with a coil having an inductance of 25 μH

What should be the capacitance of the capacitor so that, with a coil having an inductance of 25 μH, it can be tuned to resonance at a wavelength of 100 m?

Data: L (coil inductance) = 25 μH (25 * 10 ^ -6 H); λ (required wavelength) = 100 m.

Reference values: Vc (speed of light) = 3 * 10 ^ 8 m / s.

The required capacitance of the capacitor can be expressed from the equality: ν = Vc / λ = 1 / (2Π * √ (L * C)), whence 2Π * √ (L * C) = λ / Vc; √ (L * C) = λ / (Vc * 2Π); L * C = λ ^ 2 / (Vc ^ 2 * 4Π ^ 2) and C = λ ^ 2 / (Vc2 * 4Π ^ 2 * L).

Calculation: C = 100 ^ 2 / ((3 * 10 ^ 8) ^ 2 * 4 * 3.14 ^ 2 * 25 * 10 ^ -6) = 1.13 * 10 ^ -10 F = 113 pF.

Answer: The capacitance of the capacitor should be 113 pF.