# Free undamped oscillations are performed in an ideal oscillatory circuit. Ripple period 0.2 ms.

Free undamped oscillations are performed in an ideal oscillatory circuit. Ripple period 0.2 ms. Determine the amplitude of the charge fluctuation if the amplitude of the current fluctuation is 31.4 mA

Oscillations of the charge Q in the oscillatory circuit occur according to the harmonic law:
Q = Qmax * sin (wt + a),
where Qm is the amplitude of charge oscillations,
w – circular frequency,
t – time,
a – phase shift.
The current I can be found as the time derivative t of the charge Q:
I = dQ / dt = wQmax * cos (wt + a).
The maximum current will be at cos (wt + a) = 1.
Im = wQm;
Circular frequency through period T:
w = 2 * pi / T;
Im = 2 * pi * Qm / T;
Qm = (Im * T) / (2 * pi) = (0.0314 A * 0.0002 s) / (2 * 3.14) = 1 * 10⁻⁶ Cl.
Answer: The amplitude of charge fluctuations is 1 * 10⁻⁶ C (1 μC).

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