How many times will the frequency of natural oscillations in the oscillatory circuit change if the capacitance of the capacitor

| August 15, 2021 | education

How many times will the frequency of natural oscillations in the oscillatory circuit change if the capacitance of the capacitor is increased 25 times and the inductance of the coil is increased 16 times.

Natural vibration frequency:
n = 1 / Т = 1 / (2 * Π * sqrt (L * C)), L is the inductance of the coil, C is the capacitance of the capacitor.
Oscillation frequency before changes:
n1 = 1 / (2 * Π * sqrt (L1 * C1)).
Oscillation frequency after changes:
n2 = 1 / (2 * Π * sqrt (L2 * C2)), where L2 = 16 L1, C2 = 25C1.
Changing the vibration frequency:
n2 / n1 = 1 / (2 * Π * sqrt (L2 * C2)) / (1 / (2 * Π * sqrt (L1 * C1))) = sqrt (L1 * C1) / (sqrt (L2 * C2) ) = sqrt (L1 * C1) / (sqrt (16L1 * 25C1)) = sqrt (L1 * C1) / (sqrt (400L1 * C1)) = 1/20.
Answer: The vibration frequency will decrease 20 times.



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