The frequency of free electrical oscillations in the oscillating circuit is 10 MHz.

| September 7, 2021 | education

The frequency of free electrical oscillations in the oscillating circuit is 10 MHz. Calculate the frequency of oscillation in the circuit if the inductance of the coil has increased by 4 times.

To find the value of the vibration frequency in the specified circuit, we use the formula: ν = 1 / (2 * Π * √ (L * C)), whence we express: L * C = 1 / (ν ^ 2 * 2 * Π) and L * ν2 = 1 / (C * 4 * Π ^ 2). Therefore, you can use the equality: L1 * ν12 = 1 / (C * 4 * Π ^ 2) = L ^ 2 * ν2 ^ 2 and ν2 = √ (L1 * ν1 ^ 2 / L ^ 2).

Variables: L2 (final inductance of the coil) = 4L1 (initial inductance); ν1 is the initial frequency of free electrical oscillations (ν1 = 10 MHz = 10 * 106 Hz).

Calculation: ν2 = √ (L1 * ν1 ^ 2 / L ^ 2) = √ (L1 * (10 * 10 ^ 6) ^ 2 / 4L1) = 5 * 10 ^ 6 Hz = 5 MHz.

Answer: A. The frequency of free electrical oscillations will decrease to 5 MHz.



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