In an ideal oscillating circuit, the amplitude of the current fluctuations in the inductor is 10 mA.

In an ideal oscillating circuit, the amplitude of the current fluctuations in the inductor is 10 mA. At time t, the current in the coil is 2mA. Find the voltage across the capacitor at this point in time. The capacitance of the capacitor is C = 10mkF, and the inductance of the coil is L = 1mH.

To find the voltage u across the capacitor at a given time, we use the law of conservation of energy: C ∙ u² / 2 + L ∙ i² / 2 = L ∙ I² / 2. Knowing that the amplitude of the current fluctuations in the inductor is I = 10 mA = 0.01 A, at time t the current in the coil is i = 2 mA = 0.002 A, the capacitance of the capacitor C = 10 μF = 0.00001 F, and coil inductance L = 1 mH = 0.001 H, we find u² = L ∙ (I² – i²) / С or u² = 0.001 ∙ (0.01² – 0.002²) / 0.00001; u ≈ 0.098 V.
Answer: ≈ 0.098 V.