Example:A 300-V dc power supply is used to charge a 25-µF capacitor. After the capacitor is fully charged, it is disconnected fromthe power supply and connected across a 10-mH inductor. The resistance in the circuit is negligible. (a) Find the frequencyand period of oscillation of the circuit. (b) Find the capacitor charge and the circuit current 1.2 ms after the inductor andcapacitor are connected. Then find for the magnetic and electric energies (c) at and (d) at t = 1.2 ms.Given:C = 25 x 106 FL = 10 x 103 Ht = 1.2 x 103 s(c) Solving for magnetic (UB) and electric (UE) energiesat time t =0.Solution:(7.5 × 10-3 C)²Us = }Li? = 0 UgQ?2(25 × 10-6 F)(a) Solving for angular frequency (w)and period (T)1.1 J201= 2. 03 x 10° rad/sLC|(10 x 10-3H)(25 x 10-6F)(d) Solving for magnetic (UB) and electric (Ue)energies at timet =1.2 ms.2.03 x 10³ rad2n2nUB = Li? = }(1o × 10-3 H)(-10 A)² = 0.5 J= 320 Hzq? _ (-5.5 × 10-3 C)²UE13.1 x 10³s0.6 JT = .320 Hz202(25 x 10-6 F)(b) Solving for capacitor charge (q) and circuit current (i)Q = CVm = (25 x 10-6F)(300 V) = 7.5 x 10-³Csince there is no initial given charge so = 0. Therefore:q = Qcos(wt + $) = (7.5 10¬°C)cos [(2.03 x 10°rad/s)(3.1 x 10-³s) + 0] = -5.5 x 10-3 Ci = -wQsin(wt + ¢) = -(2.03 x 10³rad/s)(7.5 10¬³C)sin [(2.03 x 10³rad/s)(3.1 x 10-3s) + 0] = -10 AActivity:If a 500-V dc power supply is used to charge a 25-µF capacitor. After the capacitor is fully charged, it is disconnected fromthe power supply and connected across a 20-mH inductor. The resistance in the circuit is negligible. (a) Find the frequencyand period of oscillation of the circuit. (b) Find the capacitor charge and the circuit current 1.6 ms after the inductor andcapacitor are connected. Then find for the magnetic and electric energies (c) at and (d) at t = 1.6 ms.

Answered: Image /qna-images/answer/9922ca2d-67c1-448c-b497-70eb50fd57ce.jpg

Example: A 300-V dc power supply is used to charge a 25-µF capacitor. After the capacitor is fully charged, it is disconnected from the power supply and connected across a 10-mH inductor. The resistance in the circuit is negligible. (a) Find the frequency and period of oscillation of the circuit. (b) Find the capacitor charge and the circuit current 1.2 ms after the inductor and capacitor are connected. Then find for the magnetic and electric energies (c) at and (d) at t = 1.2 ms. Given: C = 25 x 106 F L = 10 x 10 H t = 1.2 x 103 s (c) Solving for magnetic (UB) and electric (Ue) energies at time t =0. Solution: (7.5 x 10-3 C)2 (a) Solving for angular frequency (w)and period (T) Us = }Li? = 0 Ug 1.1 J 20 2(25 x 10-6 F) 1 = 2.03 x 10° rad/s LC |(10 x 10- H)(25 x 10-6F) (d) Solving for magnetic (UB) and electric (UE) energies at timet =1.2 ms. 2. 03 x 10³ rad Ug = Li? = (10 × 10-3 H)(-10 A)² = 0.5 J 2n 2n 320 Hz 1 3.1 x 10³s q?_ (-5.5 x 10-3 C)² UE 20 0.6 J %3D 320 Hz 2(25 x 10-6 F) (b) Solving for capacitor charge (q) and circuit current (i) Q = CVm = (25 x 10-6F)(300 V) = 7.5 x 10-³C since there is no initial given charge so = 0. Therefore: q = Qcos(wt + +) = (7.5 10-°C)cos [(2.03 x 10°rad/s)(3.1 x 10-3s) + 0] = -5.5 x 10-3 C i = -wQsin(wt + ¢) = -(2.03 x 10°rad/s)(7.5 10³C)sin [(2.03 x 10³rad/s)(3.1 x 10-3s) + 0] = -10 A Activity: If a 500-V dc power supply is used to charge a 25-uF capacitor. After the capacitor is fully charged, it is disconnected from the power supply and connected across a 20-mH inductor. The resistance in the circuit is negligible. (a) Find the frequency and period of oscillation of the circuit. (b) Find the capacitor charge and the circuit current 1.6 ms after the inductor and capacitor are connected. Then find for the magnetic and electric energies (c) at and (d) at t = 1.6 ms.

18th Edition

ISBN:9781938168161

Author:OpenStax

Publisher:OpenStax

Chapter14: Inductance

Section: Chapter Questions

Problem 82CP: A coaxial cable has an inner conductor of radius a, and outer thin cylindrical shell of radius b. A...