When measuring the inductance of the coil, the frequency of electrical oscillations in the circuit turned

univerkov | April 4, 2021 | education

When measuring the inductance of the coil, the frequency of electrical oscillations in the circuit turned out to be 1 MHz. The capacity of the reference capacitor is 200 pF. What is the inductance of the coil?

v = 1 MHz = 1 * 10 ^ 6 Hz.

C = 200 pF = 2 * 10 ^ (- 10) F.

L =? Mr.

Let’s write down Thomson’s formula:

T = 2 * pi * sqrt (LC).

v = 1 / T = 1 / (2 * pi * sqrt (LC)).

Let’s square both sides.

v ^ 2 = 1 / (4 * pi ^ 2 * LC).

L = 1 / (4 * pi ^ 2 * LC * v ^ 2).

L = 1 / (4 * 3.14 ^ 2 * (10 ^ (6)) ^ 2 * 2 * 10 ^ (- 10)) =

= 1 / (4 * 9.8596 * 10 ^ (12) * 2 * 10 ^ (- 10)) = 1.3 * 10 ^ (- 4) G.

Answer: 1.3 * 10 ^ (- 4) Mr.

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