Physics 213 General PhysicsSlide 1Inductor in a CircuitRL CircuitEnergy Stored in a Magnetic FieldSlide 5Slide 6AC CircuitsAC GeneratorsResistor in an AC CircuitDissipation Across Resistors in an AC Circuitrms Current and VoltagePower RevisitedOhm’s Law in an AC CircuitCapacitors in an AC CircuitCapacitive Reactance and Ohm’s LawInductors in an AC CircuitInductive Reactance and Ohm’s LawCombined Circuits: The RLC Series CircuitCurrent and Voltage Relationships in an RLC CircuitResonance in an AC CircuitPhysics 213General PhysicsLecture 132Last Meeting: Self Inductance, RL Circuits, Energy Stored Today: Finish RL Circuits and Energy Stored. Electric Generators, Alternating CurrentInductor in a CircuitInductance can be interpreted as a measure of opposition to the rate of change in the currentRemember resistance R is a measure of opposition to the currentAs a circuit is completed, the current begins to increase, but the inductor produces an emf that opposes the increasing currentTherefore, the current doesn’t change from 0 to its maximum instantaneouslyRL CircuitWhen the current reaches its maximum, the rate of change and the back emf are zeroThe time constant, , for an RL circuit is the time required for the current in the circuit to reach 63.2% of its final value /1tI eR Energy Stored in a Magnetic FieldThe emf induced by an inductor prevents a battery from establishing an instantaneous current in a circuitThe battery has to do work to produce a currentThis work can be thought of as energy stored by the inductor in its magnetic fieldPEL = ½ L I2A long, straight wire is in the same plane as a rectangular, conducting loop.The wire carries a constant current I as shown in the figure. Which one of the following statements is true if the wire is suddenly moved toward the loop?(a) There will be no induced emf and no induced current.(b) There will be an induced emf, but no induced current.(c) There will be an induced current that is clockwise around the loop.(d) There will be an induced current that is counterclockwise around the loop.(e) There will be an induced electric field that is clockwise around the loop.XA long, straight wire is in the same plane as a rectangular, conducting loop.The wire carries a constant current I as shown in the figure. Which one of the following statements is true if the wire is suddenly moved toward the loop?(a) There will be no induced emf and no induced current.(b) There will be an induced emf, but no induced current.(c) There will be an induced current that is clockwise around the loop.(d) There will be an induced current that is counterclockwise around the loop.(e) There will be an induced electric field that is clockwise around the loop.XAC CircuitsAn AC circuit consists of a combination of circuit elements and an AC generator or sourceThe output of an AC generator is sinusoidal and varies with time according to the following equationΔv = ΔVmax sin 2ƒtΔv is the instantaneous voltageΔVmax is the maximum voltage of the generatorƒ is the frequency at which the voltage changes, in HzAC GeneratorsThe emf generated by the rotating loop can be found byε =2 B ℓ v=2 B ℓvsin θIf the loop rotates with a constant angular speed, ω, and N turnsε = N B A ω sin ω tε = εmax when loop is parallel to the fieldε = 0 when when the loop is perpendicular to the fieldResistor in an AC CircuitConsider a circuit consisting of an AC source and a resistorThe graph shows the current through and the voltage across the resistorThe current and the voltage reach their maximum values at the same timeThe current and the voltage are said to be in phaseDissipation Across Resistors in an AC CircuitThe rate at which electrical energy is dissipated in the circuit is given by P=i2R=v2/RWhere I and v are the instantaneous current and voltage across resistorThe maximum current occurs for a small amount of timeAverage current is zero.Average power > zero.rms Current and VoltageThe rms current is the direct current that would dissipate the same amount of energy in a resistor as is actually dissipated by the AC currentAlternating voltages can also be discussed in terms of rms valuesmaxmax0.7072rmsII I maxmax0.7072rmsVV V Power RevisitedThe average power dissipated in resistor in an AC circuit carrying a current I is 2av rmsI R Ohm’s Law in an AC Circuitrms values will be used when discussing AC currents and voltagesMany of the equations will be in the same form as in DC circuitsOhm’s Law for a resistor, R, in an AC circuitΔVR,rms = Irms RAlso applies to the maximum values of v and iCapacitors in an AC CircuitThe current reverses directionThe voltage across the plates decreases as the plates lose the charge they had accumulatedThe voltage across the capacitor lags behind the current by 90°Capacitive Reactance and Ohm’s Lawcapacitive reactanceWhen ƒ is in Hz and C is in F, XC will be in ohmsOhm’s Law for a capacitor in an AC circuitΔVC,rms = Irms XC12 ƒCXCInductors in an AC CircuitConsider an AC circuit with a source and an inductorThe current in the circuit is impeded by the back emf of the inductorThe voltage across the inductor always leads the current by 90°v = L I/tInductive Reactance and Ohm’s Lawinductive reactance XL = 2ƒLWhen ƒ is in Hz and L is in H, XL will be in ohmsOhm’s Law for the inductorΔVL,rms = Irms XLCombined Circuits: The RLC Series CircuitThe resistor, inductor, and capacitor can be combined in a circuitThe current in the circuit is the same at any time and varies sinusoidally with timeCurrent and Voltage Relationships in an RLC CircuitThe instantaneous voltage across the resistor is in phase with the currentThe instantaneous voltage across the inductor leads the current by 90°The instantaneous voltage across the capacitor lags the current by 90°Resonance in an AC CircuitResonance occurs at the frequency, ƒo, where the current has its maximum valueTo achieve maximum current, the impedance must have a minimum valueThis occurs when XL = XCThen,
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