p2f10_lec07_ac_circuits_and_waves

p2f10_lec07_ac_circuits_and_waves - PHYS 1200 Fall 2010...

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Unformatted text preview: PHYS 1200 Fall 2010 Lecture 07 AC Circuits three simple circuits resistor, RL, RC, RLC power in ac circuits Waves and wave motion 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 = = + 1 v 2 v Add phasors just like vectors. t Definition: Reactance 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 = = + = 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 = = = = = Reactance: current and voltage are in phase ac analysis of a capacitive load ( 29 ( ) 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 = = = = = = = + = = 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. ac analysis of an inductive load ( ) 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 = = = = = - = = 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. A useful definition: Root mean square of a sinusoidal voltage ( 29 ( 29 2 2 2 2 2 2 ( ) 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 = = = = = = = = average V M V 2 V 2 /2 2 pp M V V = Power in ac circuits The instantaneous power flowing into or out of a device is the product of the voltage and current....
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This note was uploaded on 10/17/2011 for the course PHYS 1010 taught by Professor Schroeder during the Spring '07 term at Rensselaer Polytechnic Institute.

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p2f10_lec07_ac_circuits_and_waves - PHYS 1200 Fall 2010...

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