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p2f10_lec07_ac_circuits_and_waves

# p2f10_lec07_ac_circuits_and_waves - PHYS 1200 Fall 2010...

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PHYS 1200 Fall 2010 Lecture 07 AC Circuits three simple circuits » resistor, RL, RC, RLC power in ac circuits Waves and wave motion

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Demonstrations AC circuits with Capacitors and Inductors Mobile Card apps Mass on a spring analog to RLC
Adding ac voltages around a loop When we want to add instantaneous voltages around a loop we need to keep the phase in mind. 1 1 2 2 ( ) sin( ) ( ) sin( ) v t V t v t V t ϖ ϖ φ = = + 1 v 2 v Add phasors just like vectors. t ϖ

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Definition: Reactance 0 0 0 0 In an ac circuit we have voltage: ( ) sin and current: ( ) sin( ) The ratio of the magnitudes: is called the REACTANCE. It has the same units ( ) as resistance. v t V t i t I t V X I ϖ ϖ φ = = + =
ac analysis of a resistive load ( ) sin ( ) sin R R R R v t V t v V i t t R R X R V I R ϖ ϖ = = = = = Reactance: current and voltage are “in phase”

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ac analysis of a capacitive load ( 29 0 ( ) sin sin cos cos sin 1/ 2 1 C C C C C C C C C C C C C C v t V t q Cv CV t dq i CV t dt V t I t C X C V I X ϖ ϖ ϖ ϖ π ϖ ϖ ϖ ϖ = = = = = = = + ÷ = = Reactance: Note that the current through a capacitor is 90 out of phase with voltage.
iClicker question 7.01 For which of the following frequencies is the reactance of a capacitor the largest? a)1 Hz b)100 Hz c)1000 Hz d)There is insufficient information to answer this question.

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ac analysis of an inductive load 0 ( ) sin 1 sin cos L L L L L L L L L L L L di v t V t L dt V V i di v dt tdt t L L L X L V I X ϖ ϖ ϖ ϖ ϖ = = = = = - = = Reactance: Note that the current through an inductor is 90 out of phase with voltage.
iClicker question 7.02 For which of the following frequencies is the reactance of an inductor the largest? a)1 Hz b)100 Hz c)1000 Hz d)There is insufficient information to answer this question.

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1 A useful definition: Root mean square of a sinusoidal voltage ( 29 ( 29 2 2 0 2 2 2 2 0 0 ( ) sin 2 1 ( ) 1 2 ( ) sin ( ) 2 2 M pp m T rms T T M M M rms v t V t V V amplitude V v v t dt T V V v t dt t dt T T T V V ϖ π = = = = = = = = average V M V 0 2 V 0 2 /2 2 pp M V V =
1 Power in ac circuits The instantaneous power flowing into or out of a device is the product of the voltage and current. 2 2 2 2 2 2 ( ) ( ) ( ) ( ) sin 1 sin 2 R R rms R R Ravg onecycle p t i t v t V p t iv t R V V V P tdt R R R ϖ ϖ = = = = = = For a resistor:

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1 Power in capacitors In capacitors, the current is 90 o out of phase with the voltage.
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