Question

For part (c) of the Check Your Understanding 14.10 I got 1800 rad/s for the angular frequency, am I right? The book gives the answer as 1.4 * 10^3 rad/s. Also for part (b) I got -pi/2 rad, but the answer is pi/2 rad and -pi/2 rad. I'm not sure where the pi/2 came from. I've attached the problem below. Please don't solve the example but the questions after it.

Example 14.6 An LC Circuit In an LC circuit, the self-inductance is 2.0x 10-2 H and the capacitance is 8.0x 10-6 F. At 0, all of the energy is stored in the capacitor, which has charge 1.2 × 10-) C. (a) What is the angular frequency of the oscillations in the circuit? (b) What is the maximum current flowing through circuit? (c) How long does it take the capacitor to become completely discharged? (d) Find an equation that represents q(t) Strategy The angular frequency of the LC circuit is given by Equation 14.41. To find the maximum current, the maximum energy in the capacitor is set equal to the maximum energy in the inductor. The time for the capacitor to become discharged if it is initially charged is a quarter of the period of the cycle, so if we calculate the period of the oscillation, we can find out what a quarter of that is to find this time. Lastly, knowing the initial charge and angular frequency, we can set up a cosine equation to find q(t). Solution a. From Equation 14.41, the angular frequency of the oscillations is a)-\LC- -2.5 x 10 rad/s 12.0× 10-2 H)(8.0× 10-6 F) b. The current is at its maximum lo when all the energy is stored in the inductor. From the law of energy conservation, SO 0 (2.5 x 103 rad/s)(1.2 x 10 C) 3.0x 10-2 A LC This result can also be found by an analogy to simple harmonic motion, where current and charge are the velocity and position of an oscillator C. The capacitor becomes completely discharged in one-fourth of a cycle, or during a time T/4, where T is the period of the oscillations. Since 2 o2.5 x 10 rad/s 2a = 2.5x 10-3 s.
​​​​​​​

Answer 1

W = 1/squareroot LC so C = 1/w^2 L capacitance = 2.5 micro Farad if a second identical capacitor is connected in parallel then effective capacitance will be = 2C = 5 micro farad and then frequency oscillations in the circuit will be = w^1 = w/squareroot 2 = 1.4 times 1063 rad/s at t = 0 if all the energy is stored in inductor then as i(t) = V squareroot C/squareroot L sin (wt) The capacitor first discharges through the inductor (VC(t) decreases and�i(t) increases). When w t reaches pi/2, the capacitor is fully discharged (VC = 0) and the maximum current flows in the inductor. Then the capacitor is charged again (by the current flowing in the inductor) into the reverse polarity (VC (t) reaches -V when w t reaches pi), and then discharges again (fully discharged when w t�reaches 3 pi/2) and recharges to the original polarity of VC = V when w t reaches 2

so

capacitance = 2.5 micro Farad

if a second identical capacitor is connected in parallel then effective capacitance will be = 2C = 5 micro farad

and then frequency oscillations in the circuit will be = = 1.4 x 10³ rad/s

at t= 0 if all the energy is stored in inductor

then as i(t) =

The capacitor first discharges through the inductor (VC(t) decreases and i(t) increases). When ωt reaches π/2, the capacitor is fully discharged (VC = 0) and the maximum current flows in the inductor. Then the capacitor is charged again (by the current flowing in the inductor) into the reverse polarity (VC(t) reaches -V when ωt reaches π), and then discharges again (fully discharged when ωt reaches 3π/2) and recharges to the original polarity of VC = V when ωt reaches 2π. The cycle repeats itself with the period in time (t)

so

please rate it up thanks :)