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.

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter33: Inductors And Ac Circuits

Section: Chapter Questions

Problem 11PQ

See similar textbooks

Similar questions

In an oscillating RLC circuit, R = 7.0 L. = 10 mH. And C = 3.0 F. Initially, the capacitor has a charge of 8.0 C and the current is zero. Calculate the charge on the capacitor (a) five cycles later and (b) 50 cycles later.
A step-up transformer is designed so that the output of its secondary winding is 2000 V(rms) when the primary winding is connected to a 110-V (rms) line voltage, (a) If there are 100 turns in the primary winding, how many turns are there in the secondary winding? (b) If a resistor connected across the secondary winding draws an rms current of 0.75 A. what is the current in die primary winding?
When a camera uses a flash, a fully charged capacitor discharges through an inductor. In what time must the 0.100-A current through a 2.00-mH inductor be switched on or off to induce a 500-V emf?
A 2.0-F capacitor is charged to a potential difference of 12.0 V and then connected across a 0.40-mH inductor. What is the current in the circuit when the potential difference across the capacitor is 6.0 V?
A series RLC circuit has resistance R = 50.0 and inductance L. = 0.500 H. (a) Find the circuits capacitance C if the voltage source operates at a frequency of f = 60.0 Hz and the impedance is Z = R = 50.0 . (b) What is the phase angle between the current and the voltage?
The self-inductance and capacitance of an oscillating LC circuit are L = 20 mH and C = 1.0 F , respectively. (a) What is the frequency of the oscillation? (b) If the maximum potential difference the plates of the capacitor is 50 V, what is the maximum current in the circuit?
Can a circuit e1eent have both capacitance and inductance?
Check Your Understanding In an RLC circuit, L = 5.0 mH, C=60F , and R=200 . (a) Is the circuit under damped, critically damped, or overdamped? (b) If the circuit starts oscillating with a charge of 3.0103C on the capacitor, how much energy has been dissipated in the resistor by the time the oscillations cease?
A 5-µF capacitor is charged to 30 V and is then connected in series with a 10-µH inductor and a 50-Ω resistor. The potential difference across the inductor after a long time has passed will be Group of answer choices 7 V 15 V 0 some value that cannot be determined from the given information. 30 V
A circuit consists of a 40 Ω resistor and a690 mH inductor connected in series to a 14 Vbattery. What is the value of the current when thecurrent is increasing at the rate of 7 A/s?Answer in units of A
In the circuit given below, ww wn A) When the switch is in position 2 at t = 1 second, the current (Ic) and voltage (Vc) in the capacitor depend on Find the mathematical expression. B) What is the capacitor current (Ic) and voltage (Vc) at t = 2t seconds. C) If the switch is set to position 2 at t = 2t ', it is necessary for the time dependent change of voltage (Vc) across the capacitor. Find the mathematical expression. D) Draw the time-dependent waveform of the voltage determined for the wwwm conditions in items A, B and C. w w ic 4 mA + 5 kΩ R2 R 10 μFυc 1 kN R3 3 kΩ
Discharging Capacitor: Kirchoff's loop rule applied to the discharging capacitor circuit gives Q ΣAV₁ = loop = IR- = 0 The current is leaving the positive plate so I = -dQ/dt = -CdAVc/dt. Substituting this into loop rule gives a differential equation for Q(t): RC + AVc = 0 dAvc dt This is the simplest differential equation you will learn in your differential equations class. The solution for the differential equation for AVC (t) is an exponential: R www C AV (t) = AV e-t/(RC) (discharging) where AV, is the voltage across the capacitor when discharge begins (t = 0). The quantity Tc = RC has dimensions of time and is called the time constant of the circuit. It describes how long it takes for the capacitor to charge or discharge. 2. Show that a ohm farad is the same as a second. Show steps.