An LRC oscillator circuit consists of a 50-$\varOmega$ resistor and a 1-mH inductor.What capacitance is necessary for the decay rate of the circuit (the 1/e value)to be equal to the oscillation period?
A)10 nF
B)20 nF
C)30 nF
D)40 nF
E)50 nF

Question

Quizplus · Accepted Answer

The decay rate is given by $ \tau = 2L/R $ and the oscillation period by $ T = 2\pi\sqrt{LC} $. Setting $ \tau = T $, we solve for $ C $ using $ 2L/R = 2\pi\sqrt{LC} $. Substituting $ L = 1 $ mH and $ R = 50 $ $\Omega$, we find $ C \approx 10 $ nF.

An LRC Oscillator Circuit Consists of a 50- Ω\varOmegaΩ Resistor and a 1-MH Inductor

An LRC Oscillator Circuit Consists of a 50- $\varOmega$ Resistor and a 1-MH Inductor