L-C Oscillations. A capacitor with capacitance 5.50 10 -5 F is charged by connec
ID: 1615525 • Letter: L
Question
L-C Oscillations. A capacitor with capacitance 5.50 10-5 F is charged by connecting it to a 12.0 V battery. The capacitor is disconnected from the battery and connected across an inductor with L = 1.55 H.
(a) What are the angular frequency of the electrical oscillations and the period of these oscillations (the time for one oscillation)?
_______________ rad/s
_______________ s
(b) What is the initial charge on the capacitor?
________________ C
(c) How much energy is initially stored in the capacitor?
________________ J
(d) What is the charge on the capacitor 0.0230 s after the connection to the inductor is made?
________________ C
Interpret the sign of your answer.
(e) At the time given in part (d), what is the current in the inductor?
________________ A
Interpret the sign of your answer.
(f) At the time given in part (d), how much electrical energy is stored in the capacitor and how much is stored in the inductor?
______________ J (capacitor)
_____________ J (inductor)
Explanation / Answer
a) w = 1/ sqroot (LC) = 1/ sqroot (5.50 x 10^-5 x 1.55) = 108.306 rad/sec
w= 2pi f
f = w/2pi = 17.246 hz
T = 1/f= 0.06 s apprx
b) Q = CV = 5.50 x 10^-5 (12) = 66x 10^-6 C
c)Energy = Q^2/ 2C = ( 66 x 10^-6)^2 / 2 x 5.50 x 10^ -5 = 396 x 10^ -7 J
d) q= Q cos wt = 66x 10^-6 cos ( 108.306x 0.0230 ) = -52. 519 x 10^-6 C ( -ve sign indicate change in polarity)
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