All Problems

Electric Oscillations

Problem 4.130

An oscillating circuit consisting of a coil and a capacitor connected in series is fed an' alternating emf, with coil inductance being chosen to provide the maximum current in the circuit. Find the quality factor of the system, provided an \(n\) -fold increase of inductance results in an \(\eta\) -fold decrease of the current in the circuit.

Reveal Answer
Q=η21(n1)214Q=\sqrt{\frac{\eta^{2}-1}{(n-1)^{2}}-\frac{1}{4}}