All Problems

Electric Oscillations

Problem 4.111

An oscillating circuit incorporates a leaking capacitor. Its capacitance is equal to CC and active resistance to R.R . The coil inductance is L.L . The resistance of the coil and the wires is negligible. Find: (a) the damped oscillation frequency of such a circuit; (b) its quality factor.

Reveal Answer
4.111. (a) ω=1LC−14R2C2\omega=\sqrt{\frac{1}{L C}-\frac{1}{4 R^{2} C^{2}}}; (b) Q=124R2CL−1Q=\frac{1}{2} \sqrt{\frac{4 R^{2} C}{L}-1}. When solving the problem, it should be taken into account that dq/dt=I−I′,d q / d t=I-I^{\prime}, where qq is the charge of the capacitor, II is the current in the coil winding, I′I^{\prime} is the leakage current (I′=V/R)\left(I^{\prime}=V / R\right).
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