Question

An LC circuit like the one in the figure below contains an 80.0 mH inductor and a 30.0 µF capacitor that initially carries a 175 µC charge. The switch is open for t < 0 and is then thrown closed at t = 0.

A rectangular loop forms an L C circuit. The left side of the loop contains a capacitor C carrying a charge Q_max, with the positively charged plate above the negatively charged plate. The right side of the loop contains an inductor L. The bottom side of the loop contains an open switch S.

(a)

Find the frequency (in hertz) of the resulting oscillations.

Hz

(b)

At t = 1.00 ms, find the charge on the capacitor.

What equation describes the oscillation of the charge as a function of time? µC

(c)

At t = 1.00 ms, find the current in the circuit.

If you know the charge on the capacitor as a function of time, how do you determine the current? mA

(d)

What If? What are the first three times (in ms), after

t = 0,

when the capacitor is fully charged again?

smallest value ms ms largest value ms

Answer 1

ve v oxio Coxo = 645.5 redis = 645.5 rad's / Box 10-3x30x10-6 2T 9amco f=W=645.5 -102.73 H2 6) from Q=Qm Coswt. Q - (175) Cos (645.5 x ]X10-3) Q=(139-8 uc c) I= da =¢ 1Qm Coswt) = - Wambin/wt) I =-645.5x (175x10-6) sin 1645.5 XIX 10°3) - I = (-67.96 mA d) Given Q = Qmox > Qmox = Qmox Cos/wt) Wt=1051(1) = na t = na n=1 > t = T = 4.867/ms 645.5 - n=2=7 t = 211 = 19.734 ms 645.5 n=3 7 t = 35 = [ 14.6 posms 645.5