Slide 1Next week: Prof. Claude PruneauLightning ReviewReview exampleInductor in a Circuit20.9 Energy stored in a magnetic fieldExample: stored energySlide 8Chapter 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 inductors1101/14/1901/14/19General Physics (PHY 2140)Lecture 19Lecture 19 Electricity and MagnetismInduced voltages and inductionEnergyAC circuits and EM wavesResistors in an AC circuitsChapter 20-21http://www.physics.wayne.edu/~apetrov/PHY2140/2201/14/1901/14/19Next week: Prof. Claude PruneauNext week: Prof. Claude PruneauLectures on Monday and WednesdayExam on Friday3301/14/1901/14/19Lightning ReviewLightning ReviewLast lecture: 1.1.Induced voltages and inductionInduced voltages and inductionGenerators and motorsGenerators and motorsSelf-inductionSelf-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? cosBA qF =ILtD=-DENLIF=mvrqB=4401/14/1901/14/19NSSvchangeReview exampleReview exampleDetermine the direction of current in the loop for bar magnet moving down.Initial fluxFinal fluxBy Lenz’s law, the induced field is this5501/14/1901/14/19Inductor in a CircuitInductor in a CircuitInductanceInductance can be interpreted as a can be interpreted as a measure of opposition to the measure of opposition to the rate of changerate of change in the current in 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 the As a circuit is completed, the current begins to increase, but the 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 =ER6601/14/1901/14/1920.9 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 energy212LPE LI=Summary of the properties of circuit elements.Resistor Capacitor Inductorunitsohm,  = V / Afarad, F = C / V henry, H = V s / Asymbol R C Lrelation V = I R Q = C Vemf = -L (I / t)power dissipatedP = I V = I² R = V² / R0 0energy stored 0PEC = C V² / 2 PEL = L I² / 27701/14/1901/14/19Example: stored energyExample: stored energyA 24V battery is connected in series with a resistor and an inductor, A 24V battery is connected in series with a resistor and an inductor, where R = 8.0where R = 8.0 and 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.8801/14/1901/14/19A 24V battery is connected in series with a resistor and an inductor, where R = A 24V battery is connected in series with a resistor and an inductor, where R = 8.08.0 and L = 4.0H. Find the energy stored in the inductor when the current and L = 4.0H. Find the energy stored in the inductor when the current reaches its maximum value.reaches its maximum value.Given:V = 24 VR = 8.0 L = 4.0 H Find:PEL =?Recall that the energy stored in th inductor is212LPE LI=The only thing that is unknown in the equation above is current. The maximum value for the current isInserting this into the above expression for the energy gives max243.08.0V VI AR= = =W( ) ( )214.0 3.0 182LPE H A J= =Chapter 21Chapter 21Alternating Current Circuits Alternating Current Circuits and Electromagnetic Wavesand Electromagnetic Waves101001/14/1901/14/19AC CircuitAC CircuitAn AC circuit consists of a combination of circuit elements and an An AC circuit consists of a combination of circuit elements and an AC generator or sourceAC generator or sourceThe output of an AC generator is sinusoidal and varies with time The output of an AC generator is sinusoidal and varies with time according to the following equationaccording to the following equationΔV = ΔVΔV = ΔVmaxmax sin 2 sin 2ƒtƒtΔv is the instantaneous voltageΔv is the instantaneous voltageΔVΔVmaxmax is the maximum voltage of the generator is the maximum voltage of the generatorƒ is the frequency at which the voltage changes, in Hzƒ is 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 = Imaxmax sin 2 sin 2ƒtƒt111101/14/1901/14/19Resistor 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 asΔV = ΔVΔV = ΔVmaxmax sin 2 sin 2ƒtƒtSame thing about the currentSame thing about the currentI = II = Imaxmax sin 2 sin 2ƒtƒt121201/14/1901/14/19More 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