The oscillating circuit contains a capacitor with a capacity of C = 2.6 pF and a coil with an inductance of L = 12 μH.

The oscillating circuit contains a capacitor with a capacity of C = 2.6 pF and a coil with an inductance of L = 12 μH. Determine the number of oscillations n that occurred in this circuit during the time interval Δt = 2.0ms.

Step one.

First, we need to determine what the oscillation period will be, if from the condition of our task we know for sure that the capacitance of the capacitor is 2.6 pF, while the inductance of the coil is 12 μH:

T = 2 * π * √ (L * C);

T = 2 * 3.14 * √ (2.6 * 10-12 * 12 * 10-6) = 6.28 * √ (31.2 * 10-18) ≈ 35.1 * 10-9;

Step two.

Now we can determine how many oscillations have occurred:

T = t / N;

N = t / T;

1 ms = 1 s * 10-3;

N = 2 * 10-3: 35.1 * 10-9 ≈ 56980.

Answer: 56980.