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 ω 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)

Answer 1

Capacitive c = 5.5 times 10^-5 F potential difference v = 12 v inductance l = 1.55 h Angular frequency w = 1/ squareroot lc = 1/1.55 times 5.5 times 10^-5 = 108.3 rad/s period of oscillations t = 2 pi/w = 2(22/7) /108.3 = 58.01 times 10^-3 sec Initial charge Q = cv = 5.5 times 10^-5 times 12 = 6.6 times 10^-4 coulomb required energy u = q^2/2c = (6.6 times 10^-4) ^2/2(5.5 times 10^-5) = 3.96 times 10^-3 j charge q = Q coswt = (6.6 times 10^-4) cos [108.3 t] time t = 0.0235 so, q = (6.6 times 10^-4) cos [108.3 times 0.023] = (6.6 times 10^-) cos (2.4909 rad) = (6.6 times 10^-4) (-0.79566) = - 5.251 times 10^-4 coulomb.