Chapt36_VG - Chapter 36 Viewgraphs AC Circuits Introduction...

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Chapter 36 Viewgraphs AC Circuits
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Most currents and voltages vary in time. The presence of circuit elements like capacitors and inductors complicates the relation between currents and voltage when these depend on time. V ( t ) = I ( t ) R I ( t ) = C d dt V c ( t ) V L ( t ) = L d dt I ( t ) Resistive element -I&V proportional Reactive elements involves derivatives Voltage and current are not simply proportional for reactive elements. Ohm’s law does not apply. Introduction
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Three categories of time behavior 1. Direct Current (DC) Voltages and currents are constants in time. Example: batteries - circuits driven by batteries 2. Transients Voltages and currents change in time after a switch is opened or closed. Changes diminish in time and stop if you wait long enough. S R L V 0 V L (t) t V L ( t ) = V 0 exp[ tR / L ]
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3. Alternating Current (AC). The voltages and currents continually change sinusoidally in time. V ( t ) = V 0 cos[ ω t + θ ] amplitude frequency phase Examples: our power grid when it is on. f=60 Hz, V=110 V (RMS) audio signals communication signals Power in microwave ovens Power in MRI machines Real Life voltages involve DC, AC and Transients
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Power Supply : converts AC to DC Present inside almost all home electronics Inverter : converts DC to AC Plugs into cigarette lighter, charges laptop. Don’t run a hair straighter on one of these while driving in your car.
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AC - Circuits First Rule of AC - Circuits - everything oscillates at the same frequency If a circuit is driven by a source with frequency ω , and you wait for all transients to die out, the circuit will reach a state where every voltage and current is oscillating at the same frequency ω . Often this is called a “steady state” even though every thing is oscillating. The problem then becomes: Find the amplitude and phase of each voltage and current.
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L c /p L c /m L c /m L c /n R c /p R c /m R c /m R c /n C c C s L s V s ( t ) = V 0 cos[ ω t + θ ] Complicated circuit: Rs, Ls, and Cs Every voltage will be in the form V n ( t ) = V 0 n cos[ ω t + θ n ] Every current will be in the form I m ( t ) = I 0 m cos[ ω t + θ m ] Problem is to find the amplitudes and phases
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Some general comments: 1. All voltages and currents oscillate at the same frequency ω . 2. Amplitudes and phases of voltages and currents depend
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This note was uploaded on 12/28/2011 for the course PHYSICS 270 taught by Professor Drake during the Fall '08 term at Maryland.

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Chapt36_VG - Chapter 36 Viewgraphs AC Circuits Introduction...

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