What capacitor should be included in the oscillatory circuit in order to obtain oscillations

| April 6, 2021 | education

What capacitor should be included in the oscillatory circuit in order to obtain oscillations with a frequency of 10 MHz with a coil inductance of 5.1 μH?

Data: L is the value of the inductance of the coil (L = 5.1 * 10 ^ -6 H (5.1 μH)); ν is the required oscillation frequency of the circuit (ν = 10 ^ 7 Hz (10 MHz)).

To find out the required capacitance of the capacitor for the circuit, consider the formula: ν = 1 / (2 * Π * √ (L * Cx)), whence we express: √ (L * Cx) = 1 / (ν * 2 * Π), L * Cx = 1 / (ν2 * 4 * Π ^ 2) and Cx = 1 / (L * ν ^ 2 * 4 * Π ^ 2).

Let’s perform the calculation: Cx = 1 / (L * ν ^ 2 * 4 * Π ^ 2) = 1 / (5.1 * 10 ^ -6 * (10 ^ 7) ^ 2 * 4 * 3.14 ^ 2) ≈ 4.97 * 10 ^ -11 F or 49.7 pF.

Answer: A 49.7 pF capacitor must be included in the circuit.



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