The frequency of oscillation of the LC circuit in the figure is 200 kHz. At time

Question

The frequency of oscillation of the LC circuit in the figure is 200 kHz. At time t=0 the upper capacitor plate has its maximum positive charge. Select True or False for all statements. At t=1.25 ?s, the charge on the lower plate has its maximum positive value. At t=1.25 ?s, the current is maximum. At t=2.50 ?s, the current is zero. At t=1.25 ?s, half the energy is stored in the capacitor, half in the inductor. At t=5.00 ?s, the energy is completely stored in the capacitor. At t=2.50 ?s, the charge on the lower plate has its maximum positive value.

Explanation / Answer

Period T = 5 us. At t=0, vC = vmax and Q = Qmax. Thus vC and Q are cos(wt) waves, and I is a -sin(wt) wave, with all periods = 5 us. The energy in the capacitor is proportional to vC^2 thus to cos(wt)^2. The energy in the inductor is proportional to I^2 thus to sin(wt)^2. 1. t = T/4 ==> cos(wt) = 0 ==> False 2. t = T/4 ==> -sin(wt) = -1/sqrt(2) ==> False 3. t = T/2 ==> sin(wt) = 0 ==> true 4. t = T/4 ==> cos(wt)^2 = 0, sin(wt)^2 = 1 ==> false 5. t = T ==> cos(wt)^2 = 1 ==> true 6. t = T/2 ==> cos(wt) = -1 ==> true

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