The period of free electromagnetic oscillations in an ideal oscillatory circuit

The period of free electromagnetic oscillations in an ideal oscillatory circuit, the capacitance of which is C = 4.9 nF, T = 1 μs. Determine the inductance L of the coil of this circuit.

Let’s turn to the Thompson formula for the period of electromagnetic oscillations in the circuit:

T = 2π√LC, where L is the inductance, C is the capacitance of the loop.

Let us express L from it, for this we square the equation:

T ^ 2 = (2π) ^ 2 * L * C;

L = T ^ 2 / (2π) ^ 2 * C.

We substitute the known values:

L = (10 ^ (- 6)) ^ 2/40 * 4.9 * 10 ^ (- 9) = 10 ^ (- 3) / 200 = 0.5 * 10 ^ (- 5) H = 5 μH.

Answer: the desired loop inductance is 5 μH.