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.

A battery is used to charge a capacitor. When the stored energy in the capacitor is 1 µj, it is disconnected from the battery in the circuit and connected in series with an inductor which has inductance of 6 µH. What is the current in the inductor when the capacitor charge is half of its initial maximum value? (Resistance is negligible.) O 0.2 A O 0.5 A O v2 A O 2 A O 20 A

What is the relationship between a sinusoidal current and a sinusoidal voltage in an inductor?

A V = 86-V source is connected in series with an R = 1.8-kΩ resistor and an L = 26-H inductor and the current is allowed to reach maximum. At time t = 0 a switch is thrown that disconnects the voltage source but leaves the resistor and the inductor connected in their own circuit. 1) How much time, in milliseconds, is needed for the current in the circuit to drop to 12 % of its value at t = 0?  2) How much energy, in millijoules, does the circuit dissipate during that time?

The charge on the capacitor of an LC circuit with capacitance C and inductance L obeys the following equation. Find the maximum current in the circuit. q= Q cos [t/(LC)0.5] Q Q/(LC) 0.5 zero QQ²/(LC) 0.5 imax 1/(LC) 0.5

An inductor and a resistor are connected in series. When connected to a 60-Hz, 90-V (rms) source, the voltage drop across the resistor is found to be 55 V (rms) and the power delivered to the circuit is 18 W. (a) Find the value of the resistance. 22 (b) Find the value of the inductance. H

A radio tune circuit consists of an inductor of inductance 0.4 H and resistance 10 Ω connected in parallel with a variable capacitor of capacitance set at 0.4 ?F. A radio signal captured by the receiver induces avoltage of 0.01 V across the inductor. Calculate the frequency of the radio waves. What is the effect of reducing the coil resistance to 5.0 Ω

In an oscillating LC circuit, the maximum charge on the capacitor is 2 x 10 °C and the maximum current through the inductor is 11 mA. (a) What is the period of the oscillations? (b) How much time elapses between an instant when the capacitor is uncharged and the next instant when it is fully charged? The period of the oscillation is The time between when charge on capacitor is zero and when it holds maximum charge is Submit answer / ms. 4 ms.