With an increase in the capacitance of the capacitor of the oscillating circuit by 0.08 μF, the oscillation

With an increase in the capacitance of the capacitor of the oscillating circuit by 0.08 μF, the oscillation frequency decreased by 3 times. Find the initial capacitance of the capacitor. The inductance of the coil remains the same.

Data: ΔC (increase in capacitor capacity) = 0.08 μF; ν1 (initial oscillation frequency) = 3ν2 (final frequency): L (inductance) = L1 = L2.

1) We transform the formula for calculating the vibration frequency: ν = 1 / (2 * Π * √ (L * C)); 1 / (2 * Π) = ν * √ (L * C).

2) Substitute the known values: ν1 * √ (L * C1) = ν2 * √ (L * C2).

ν1 / ν2 = √ (L * C2) / √ (L * C1).

3 = √ (L * C2) / √ (L * C1).

9 = (L * C2) / (L * C1).

9 = C2 / C1.

9C1 = C2.

9C1 = C1 + 0.08.

8C1 = 0.08.

C1 = 0.08 / 8 = 0.01 μF.