Next week: Prof. Claude PruneauLightning ReviewReview exampleInductor in a Circuit20.9 Energy stored in a magnetic fieldExample: stored energyChapter 21AC CircuitResistor in an AC CircuitMore About Resistors in an AC Circuitrms Current and VoltageOhm’s Law in an AC CircuitExample: an AC circuitCapacitors in an AC CircuitMore About Capacitors in an AC CircuitCapacitive Reactance and Ohm’s LawInductors in an AC CircuitInductive Reactance and Ohm’s LawExample: AC circuit with capacitors and inductors1110/22/200310/22/2003General Physics (PHY 2140)Lecture 19Lecture 19¾ Electricity and Magnetism9Induced voltages and induction9Energy9AC circuits and EM waves9Resistors in an AC circuitsChapter 20-21http://www.physics.wayne.edu/~apetrov/PHY2140/2210/22/200310/22/2003Next week: Prof. Claude Next week: Prof. Claude PruneauPruneauLectures on Monday and WednesdayExam on Friday3310/22/200310/22/2003Lightning ReviewLightning ReviewmvrqB=Last lecture:1.1.Induced voltages and inductionInduced voltages and induction99Generators and motorsGenerators and motors99SelfSelf--inductioncosBAθΦ=ILt∆=−∆ENLIΦ=inductionReview Problem: Charged particles passing through a bubble chamber leave tracks consisting of small hydrogen gas bubbles. These bubbles make visible the particles’ trajectories. In the following figure, the magnetic field is directed into the page, and the tracks are in the plane of the page, in the directions indicated by the arrows. (a) Which of the tracks correspond to positively charged particles? (b)If all three particles have the same mass and charges of equal magnitude, which is moving the fastest?4410/22/200310/22/2003SSReview exampleReview exampleDetermine the direction of current in the loop for bar magnet moving down.vNInitial fluxFinal fluxBy Lenz’s law, the induced field is thischange5510/22/200310/22/2003Inductor in a CircuitInductor in a CircuitInductanceInductancecan be interpreted as a can be interpreted as a measure of opposition to the measure of opposition to the rate rate of changeof changein the currentin the currentRemember Remember resistance R is a measure of opposition to the currentresistance R is a measure of opposition to the currentAs a circuit is completed, the current begins to increase, but tAs a circuit is completed, the current begins to increase, but the he inductor produces an inductor produces an emf that opposes the increasing currentemf that opposes the increasing currentTherefore, the current doesn’t change from 0 to its maximum Therefore, the current doesn’t change from 0 to its maximum instantaneouslyinstantaneouslyMaximum current:Maximum current:maxI =ER6610/22/200310/22/200320.9 Energy stored in a magnetic field20.9 Energy stored in a magnetic fieldThe battery in any circuit that contains a coil has to do The battery in any circuit that contains a coil has to do work to produce a currentwork to produce a currentSimilar to the capacitor, any coil (or inductor) would store Similar to the capacitor, any coil (or inductor) would store potential energypotential energy212LPELI=PEL= L I² / 2PEC= C V² / 20energy stored00P = I V = I² R = V² / Rpower dissipatedemf = -L (∆I / ∆t)Q = C VV = I RrelationLCRsymbolhenry, H = V s / Afarad, F = C / Vohm, Ω = V / AunitsInductorCapacitorResistorSummary of the properties of circuit elements.7710/22/200310/22/2003Example: stored energyExample: stored energyA 24V battery is connected in series with a resistor and an induA 24V battery is connected in series with a resistor and an inductor, ctor, where R = 8.0where R = 8.0ΩΩand L = 4.0H. Find the energy stored in the inductor and L = 4.0H. Find the energy stored in the inductor when the current reaches its maximum value.when the current reaches its maximum value.8810/22/200310/22/2003A 24V battery is connected in series with a resistor and an induA 24V battery is connected in series with a resistor and an inductor, where R = ctor, where R = 8.08.0ΩΩand L = 4.0H. Find the energy stored in the inductor when the cand L = 4.0H. Find the energy stored in the inductor when the current urrent reaches its maximum value.reaches its maximum value.Recall that the energy stored in thinductor isGiven:V = 24 VR = 8.0 ΩL = 4.0 H Find:PEL=?212LPE LI=The only thing that is unknown in the equation above is current. The maximum value for the current ismax243.08.0VVIAR== =ΩInserting this into the above expression for the energy gives ()()214.0 3.0 182LPE H A J==Chapter 21Chapter 21Alternating Current Circuits Alternating Current Circuits and Electromagnetic Wavesand Electromagnetic Waves101010/22/200310/22/2003AC CircuitAC CircuitAn AC circuit consists of a combination of circuit elements and An AC circuit consists of a combination of circuit elements and an an AC generator or sourceAC generator or sourceThe output of an AC generator is sinusoidal and varies with timeThe output of an AC generator is sinusoidal and varies with timeaccording to the following equationaccording to the following equation∆∆V = V = ∆∆VVmaxmaxsin 2sin 2ππƒƒtt∆∆v is the instantaneous voltagev is the instantaneous voltage∆∆VVmaxmaxis the maximum voltage of the generatoris the maximum voltage of the generatorƒƒis the frequency at which the voltage changes, in Hzis the frequency at which the voltage changes, in HzSame thing about the current (if only a resistor)Same thing about the current (if only a resistor)I = II = Imaxmaxsin 2sin 2ππƒƒtt111110/22/200310/22/2003Resistor in an AC CircuitResistor in an AC CircuitConsider a circuit consisting of Consider a circuit consisting of an AC source and a resistoran AC source and a resistorThe graph shows the current The graph shows the current through and the voltage across through and the voltage across the resistorthe resistorThe current and the voltage The current and the voltage reach their maximum values at reach their maximum values at the same timethe same timeThe current and the voltage The current and the voltage are said to be are said to be in phasein phaseVoltage varies asVoltage varies as∆V = ∆V = ∆V∆Vmaxmaxsin 2sin 2ππƒtƒtSame thing about the currentSame thing about the currentI = II = Imaxmaxsin 2sin 2ππƒtƒt121210/22/200310/22/2003More About Resistors in an AC CircuitMore About Resistors in an AC CircuitThe direction of the current has no effect on The direction of the current has no effect on the behavior of the resistorthe behavior of