At t = 0, the charge stored on the capacitor plates is maximum in an oscillating

Question

At

t = 0,

the charge stored on the capacitor plates is maximum in an oscillating series RLC circuit. At what time will the maximum possible energy that can be stored in the capacitor fall to one-eighth of its initial value if

R = 7.20

and

L = 20.0 H?

The differential equation for an RLC circuit is

L

+ R

+

q = 0

and the solution to this equation is

q = qmaxeRt/2L cos dt.

d2q dt2 Att 0, the charge stored on the capacitor plates is maximum in an oscillating series RICcircuit. At what time will the maximum possible energy that can be stored in the capacitor fall to one-eighth of its initial value if R 7.20 n and deg da 20.0 H? The di fferential equation for an RLC circ 0 and he hat e damp that is, assume e the resistance R 4 sqrt(AL/C so that olution to Assume s equal on is ing is very weal the amplitude of the charge does not change by much during one oscillation)

Explanation / Answer

-Rt/2L = -log(sqrt(8))

-Rt/2L = -log(8)/2

t = log(8)*L/R

t = log(8)*20/7.2

t = 0.903*20/7.2 = 2.51sec

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