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Chapter 9: Sinusoids and Phasor

Chapter 9: Sinusoids and Relationships for circuit and s Laws in the Frequency Application: Summary1 How to determine v(t)and i(t)?2vs(t) = 10 VHow can we apply what we have learned before to determine i(t)and v(t)? Motivation (1)DC Motivation (2) Theoutputofthecircuitwillconsistoftwopar ts: atransientpartthatdiesoutastimeincreases ; ,thetransientpartdiesoutquickly,perhapsi na coupleofmilliseconds. ACcircuitsarethesubjectofthischapter. Inparticular, It'susefultoassociatea complexnumberwitha Usingphasorsandimpedances,weobtainanewre presentationofthelinearcircuit,calledthe frequency-domainrepresentation. Sinusoids (1) A sinusoidis a signal that has the form of the sine or cosine function.

Euler’s identity. 8 z 1 +z 2 =(x 1 +x 2 ) +j (y 1 + y. 2) z. 1. ... • Circuits that contain inductors and capacitors are represented by differential equations. When the input to the circuit is sinusoidal, the phasors and impedances can be used to represent the circuit in the frequency domain. In the frequency domain, the

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