Chapt36_VG

# 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
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.
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
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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Chapt36_VG - Chapter 36 Viewgraphs AC Circuits Introduction...

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