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.
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.
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![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 103 H
t = 1.2 x 103 s
(c) Solving for magnetic (UB) and electric (UE) energies
at time t =0.
Solution:
(7.5 × 10-3 C)²
Us = }Li? = 0 Ug
Q?
2(25 × 10-6 F)
(a) Solving for angular frequency (w)and period (T)
1.1 J
20
1
= 2. 03 x 10° rad/s
LC
|(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 rad
2n
2n
UB = Li? = }(1o × 10-3 H)(-10 A)² = 0.5 J
= 320 Hz
q? _ (-5.5 × 10-3 C)²
UE
1
3.1 x 10³s
0.6 J
T = .
320 Hz
20
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 10³rad/s)(7.5 10¬³C)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-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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8b2aaf99-2b4f-4cea-90f9-8b4c3d884deb%2F9922ca2d-67c1-448c-b497-70eb50fd57ce%2Fnxwi1f_processed.jpeg&w=3840&q=75)
Transcribed Image Text: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 103 H
t = 1.2 x 103 s
(c) Solving for magnetic (UB) and electric (UE) energies
at time t =0.
Solution:
(7.5 × 10-3 C)²
Us = }Li? = 0 Ug
Q?
2(25 × 10-6 F)
(a) Solving for angular frequency (w)and period (T)
1.1 J
20
1
= 2. 03 x 10° rad/s
LC
|(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 rad
2n
2n
UB = Li? = }(1o × 10-3 H)(-10 A)² = 0.5 J
= 320 Hz
q? _ (-5.5 × 10-3 C)²
UE
1
3.1 x 10³s
0.6 J
T = .
320 Hz
20
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 10³rad/s)(7.5 10¬³C)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-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.
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