A capacitor C, which may be considered to be loss-free, is connected with an inductor to form a closed loop. The inductor behaves as a pure inductance L in series with a resistor R. If, when the circuit is first connected the capacitor is charged, derive the condition for oscillatory decay.
Derive an expression for the quality factor Q1 of the circuit by considering the decay of the oscillation, using the result that the amplitude falls by a factor of e in Q1/π periods.
A quality factor Q2 can also be defined in terms of the circuit parameters as ω0L/R, where ω20 = 1/LC. If C = 2 μF and L = 1 mH, calculate the maximum value of R such that Q1 and Q2 agree to better than 1 part in 103.