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Published byMelissa Carpenter Modified over 4 years ago

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AC CIRCUITS ANALYSIS

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Sinusoids A sinusoid is a signal that has the form of the sine or cosine function.

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Phasors A phasor is a complex number that represents the amplitude and phase of a sinusoid.

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Phasors

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Sinusoids to Phasor Conversion

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Resistors in an AC Circuit

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Inductors in an AC Circuit The voltage leads the current by 90 degrees.

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Capacitors in an AC Circuit The current leads the voltage by 90 degrees.

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Root Mean Square (RMS) The RMS value of a set of values (or a continuous-time waveform) is the square root of the arithmetic mean (average) of the squares of the original values (or the square of the function that defines the continuous waveform).

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Impedance and Admittance The impedance Z of a circuit is the ratio of the phasor voltage V to the phasor current I, measured in ohms. The admittance Y is the reciprocal of impedance, measured in siemens (S).

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Problems 1) 2)

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Problems 3) Determine the input impedance of the circuit at ω = 10 rad/s. Answer: 32.38 j 73.76 ohms.

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Problems 4) Use mesh analysis to determine Vo. ans: Vo = 12|_90° V

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Problems 5) Find Vx using nodal analysis. ans:Vx =17.4|_-21.62°V

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AC i-V relationship for R, L, and C Resistive Load Source v S (t) Asin t V R and i R are in phase Phasor representation: v S (t) =Asin t = Acos(

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