Presentation on theme: "Physics 2113 Jonathan Dowling"— Presentation transcript:
1 Physics 2113Jonathan DowlingLecture 33: WED 12 NOV Electrical Oscillations, LC Circuits, Alternating Current INikolai Tesla
2 What are we going to learn? A road map Electric charge Electric force on other electric charges Electric field, and electric potentialMoving electric charges : currentElectronic circuit components: batteries, resistors, capacitorsElectric currents Magnetic field Magnetic force on moving chargesTime-varying magnetic field Electric FieldMore circuit components: inductors.Electromagnetic waves light wavesGeometrical Optics (light rays).Physical optics (light waves)
4 Oscillators in Physics Oscillators are very useful in practical applications, for instance, to keep time, or to focus energy in a system.All oscillators can store energy in more than one way and exchange it back and forth between the different storage possibilities. For instance, in pendulums (and swings) one exchanges energy between kinetic and potential form.We have studied that inductors and capacitors are devices that can store electromagnetic energy. In the inductor it is stored in a B field, in the capacitor in an E field.
5 PHYS2110: A Mechanical Oscillator Newton’s law F=ma!
6 PHYS2113 An Electromagnetic LC Oscillator Capacitor initially charged. Initially, current is zero, energy is all stored in the E-field of the capacitor.Capacitor discharges completely, yet current keeps going. Energy is all in the B-field of the inductor all fluxed up.A current gets going, energy gets split between the capacitor and the inductor.The magnetic field on the coil starts to deflux, which will start to recharge the capacitor.Finally, we reach the same state we started with (withopposite polarity) and the cycle restarts.
7 Electric Oscillators: the Math Energy Cons.Or loop rule!Both give Diffy-Q:Solution to Diffy-Q:LC FrequencyIn Radians/Sec
17 Example 1 : Tuning a Radio Receiver FM radio stations: frequencyis in MHz.The inductor and capacitor in my car radio have one program at L = 1 mH & C = 3.18 pF. Which is the FM station?(a) KLSU 91.1(b) WRKF 89.3(c) Eagle 98.1 WDGL
18 Example 2 ω = 2500 rad/s T = period of one complete cycle In an LC circuit, L = 40 mH; C = 4 μFAt t = 0, the current is a maximum;When will the capacitor be fully charged for the first time?ω = 2500 rad/sT = period of one complete cycleT = 2π/ω = 2.5 msCapacitor will be charged after T=1/4 cycle i.e att = T/4 = 0.6 ms
19 Example 3In the circuit shown, the switch is in position “a” for a long time. It is then thrown to position “b.”Calculate the amplitude ωq0 of the resulting oscillating current.baE=10 V1 mH1 mFSwitch in position “a”: q=CV = (1 mF)(10 V) = 10 mCSwitch in position “b”: maximum charge on C = q0 = 10 mCSo, amplitude of oscillating current =0.316 A
20 Example 4 In an LC circuit, the maximum current is 1.0 A. If L = 1mH, C = 10 mF what is the maximum charge q0 on the capacitor during a cycle of oscillation?Maximum current is i0=ωq0 Maximum charge: q0=i0/ωAngular frequency w=1/√LC=(1mH 10 mF)–1/2 = (10-8)–1/2 = 104 rad/sMaximum charge is q0=i0/ω = 1A/104 rad/s = 10–4 C