The coil of which inductance must be included in the oscillatory circuit in order to obtain
| June 20, 2021 | education
The coil of which inductance must be included in the oscillatory circuit in order to obtain a free oscillation frequency of 2 MHz with a capacitor capacitance of 500 pF?
Frequency of oscillations in the circuit:
n = 1 / (2 * Π * √ (L * C)), where n is the value of the frequency of free oscillations (n = 2 MHz = 2 * 10 ^ 6 Hz), L is the sought inductance of the coil, C is the capacitance of the capacitor (C = 500 pF = 500 * 10 ^ -9 F).
2 * Π * √ (L * C) = 1 / n.
√ (L * C) = 1 / (n * 2 * Π).
L * C = (1 / (n * 2 * Π)) ^ 2.
L = 1 / ((n * 2 * Π) ^ 2 * C) = 1 / ((2 * 10 ^ 6 * 2 * 3.14) ^ 2 * 500 * 10 ^ -9) = 1.27 * 10 ^ -8 H = 12.7 nH.
Answer: A coil with an inductance of 12.7 nH must be included in the circuit.
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