Lect11 - AC Power Lecture 11 AC Power Circuits Voltage...

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1 Lecture 11: AC Power, Circuits AC Circuits – LCR Circuits Phasors, Impedance • Resonance – RC and RL Circuits • Filters – Motors AC and DC October 11 Physics 104, Fall 2011 1 AC Power Voltage, current and power depend on time October 11 Physics 104, Fall 2011 2 We are interested in averages ( f = 60Hz) V = V 0 sin2 π ft I = I 0 sin2 π ft P = VI = V 0 I 0 sin 2 2 π ft I rms = V rms R P ave = V rms I rms = V rms 2 R = I rms 2 R P ave = 1 2 V 0 I 0 V rms = V 0 2 I rms = I 0 2 Phasors AC circuits can be analyzed graphically An arrow has a length V max The arrow’s tail is at the origin The arrow makes an angle of θ with the horizontal The angle varies with time according to θ = 2 π ƒt The rotating arrow represents the voltage in an AC circuit The arrow is called a phasor A phasor is not a vector Provides time dependence in an AC circuit Section 22.2 October 11 3 Physics 104, Fall 2011 Resistor Phasor Diagram The current in an AC circuit can also be represented by a phasor The two phasors always make the same angle with the horizontal axis as time passes The current and voltage are in phase For a circuit with only resistors October 11 4 Physics 104, Fall 2011 Capacitor Phasor Diagram The current is out of phase with the voltage The angle π /2 is phase angle, Φ , between V and I The current and voltage are out of phase by 90 o – It takes time to build voltage across a capacitor October 11 5 Physics 104, Fall 2011 Inductor Phasor Diagram The current is out of phase with the voltage For this circuit, the current and voltage are out of phase by -90 o – Remember, for a capacitor, the phase difference was +90 o October 11 6 Physics 104, Fall 2011
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2 Impedance October 11 Physics 104, Fall 2011 7 Impedance frequency Impedance in AC Circuits R is independent of f R Impedance October 11 Physics 104, Fall 2011 8 Impedance frequency Impedance in AC Circuits R is independent of f X L increases with f R X L X L = 2 π f L Impedance October 11 Physics 104, Fall 2011 9 Impedance frequency Impedance of AC Circuits X C decreases as 1/f R X L X C •R is independent of f •X L increases with f Impedance X L = 2 π f L X C = 1 2 π f C Impedance October 11 Physics 104, Fall 2011 10 Impedance frequency Impedance of AC Circuits R is independent of f X L increases with f X C decreases as 1/f Z: X L and X C subtract R X L X C Z f 0 Impedance X L = 2 π f L X C = 1 2 π f C Z = R 2 + ( X L X C ) 2 AC Circuits Resistors: V R =IR V R and I in phase Capacitors: V C =I X C : X c = 1/(2 π f C) V C
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