In a circuit, an inductor is connected in parallel with two capacitors. The capacitors are used one at a time. Given that the inductance, L = 3.20 mH, and the capacitances are C₁ = 0.20 nF and C₂ = 0.35 nF, calculate the oscillation frequencies for each configuration.

You are provided with a 0.5 F capacitor, a long copper wire of radius 20 μm, and a hollow ceramic cylinder of radius 3.2 mm. What length of an inductor made from these materials will form a 0.20 Hz oscillator with the capacitor when the inductor has 3 layers of turns closely packed together?

A highly sensitive instrument detects nanoscale gaps by using an LC circuit with a parallel-plate capacitor having plate area A and known inductance L. The charge oscillates at a frequency f when the capacitor plates are separated by a distance x. The relationship between 𝑥, 𝜖₀, 𝐴, 𝑓, and 𝐿 is given by: x=4π²Aϵ₀f²L.

If 𝑓 is on the order of 500 kHz and can be measured to a precision of Δ𝑓=0.5 Hz, with what percent accuracy can 𝑥 be determined? Fringing effects at the capacitor’s edges are ignored.