Question

An ideal coil and an ideal capacitor can be connected in series or in parallel. The circuits so formed are fed to the same sinusoidal alternative voltage. The equivalent reactants of the circuits at the serial and parallel connection, respectively, are Xs and Xp. Knowing the coil inductance L, determine the capacitance of the capacitor.
Answer: C = L / Xs • Xp

Answer 1

Let the coil inductance be L and the capacitance of the capacitor be C.

When the ideal coil and an ideal capacitor are connected in series,

Xs = L + C

When the ideal coil and an ideal capacitor are connected in parallel,

Xp = (L/C) / (L + C)

Substituting Xs into the equation for Xp,

Xp = (L/C) / Xs

C = L / Xs • Xp