charge and the current (i) is zero, then P= 0. If q =0 at time t=0, then =±n/2.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 x 10-3 C)?(a) Solving for angular frequency (w)and period (T)Ug =Li? = 0Ug =2C- 1.1 J2(25 x 10-6 F)1= 2.03 x 10° rad/s(10 x 10-3H)(25 x 10¬°F)(d) Solving for magnetic (UB) and electric (UE)energies at time t =1.2 ms.2. 03 х 103 РadUg = }Li² = }(10 × 10-3 H)(-10 A)² = 0.5 Jf= 320 Hz%3D2nq?UF =20(-5,5 × 10-3 C)²1T == 3.1x 10-³s= 0.6 J2(25 x 10-6 F)%3D320 Hz(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¬³C)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/943f0fe3-1322-41a3-8696-490a0076af8c.jpg

Activity: If a 500-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 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.

Activity: If a 500-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 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.

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter23: Faraday’s Law And Inductance

Section23.6: Rl Circuits

Problem 23.8QQ

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