An LC circuit consists of a capacitor, C 1.72 μF, and an inductor, L 5.32 mH. The capacitor is fully charged using a battery and then connected to the inductor. An oscilloscope is used to measure the frequency of the oscillations in the circuit. Next, the circuit is opened, and a resistor, R, is inserted in series with the inductor and the capacitor. The capacitor is again fully charged using the same battery and then connected to the circuit. The angular frequency of the damped oscillations in the RLC circuit is found to be 19.5% less than the angular frequency of the oscillations in the LC circuit. a) Determine the resistance of the resistor. b) How long after the capacitor is reconnected in the circuit will the amplitude of the damped current through the circuit be 19.0% of the initial amplitude? c) How many complete damped oscillations will have occurred in that time?
We know Wo 1/sqrt(LC) 10,454 rad/s Wd is given to be 0.805*Wo Looking at the reference alpha^2 Wo^2 - Wd^2 and Wd 0.805*Wo alpha^2 Wo^2(1-0.805^2)38,465,981 alpha 6202.1 R/2L R 66 Ohms b) we can write 0.19 e^(-6202.1*t) Ln(0.19)/(-6202.1) t 0.268 milliseconds c) wd 8415.5 2pi/T T 0.747ms So it appears the current is at 19% before even one oscillation has finished unless I have an error. In an RLC ckt when the charged cap is connected, i(0) 0 All of the voltage is dropped across the inductor meaning VR0 at t0 which means i(0) 0 So not sure what initial amplitude they are talking about
Here is an earlier Answer to the same Question: .
