AC CIRCUITS ANALYSIS. Sinusoids A sinusoid is a signal that has the form of the sine or cosine...
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Transcript of AC CIRCUITS ANALYSIS. Sinusoids A sinusoid is a signal that has the form of the sine or cosine...
![Page 1: AC CIRCUITS ANALYSIS. Sinusoids A sinusoid is a signal that has the form of the sine or cosine function.](https://reader033.fdocuments.us/reader033/viewer/2022051014/55145bb4550346414e8b5642/html5/thumbnails/1.jpg)
AC CIRCUITS ANALYSIS
![Page 2: AC CIRCUITS ANALYSIS. Sinusoids A sinusoid is a signal that has the form of the sine or cosine function.](https://reader033.fdocuments.us/reader033/viewer/2022051014/55145bb4550346414e8b5642/html5/thumbnails/2.jpg)
Sinusoids
• A sinusoid is a signal that has the form of the sine or cosine function.
![Page 3: AC CIRCUITS ANALYSIS. Sinusoids A sinusoid is a signal that has the form of the sine or cosine function.](https://reader033.fdocuments.us/reader033/viewer/2022051014/55145bb4550346414e8b5642/html5/thumbnails/3.jpg)
Phasors
• A phasor is a complex number that represents the amplitude and phase of a sinusoid.
![Page 4: AC CIRCUITS ANALYSIS. Sinusoids A sinusoid is a signal that has the form of the sine or cosine function.](https://reader033.fdocuments.us/reader033/viewer/2022051014/55145bb4550346414e8b5642/html5/thumbnails/4.jpg)
Phasors
![Page 5: AC CIRCUITS ANALYSIS. Sinusoids A sinusoid is a signal that has the form of the sine or cosine function.](https://reader033.fdocuments.us/reader033/viewer/2022051014/55145bb4550346414e8b5642/html5/thumbnails/5.jpg)
Phasors
![Page 6: AC CIRCUITS ANALYSIS. Sinusoids A sinusoid is a signal that has the form of the sine or cosine function.](https://reader033.fdocuments.us/reader033/viewer/2022051014/55145bb4550346414e8b5642/html5/thumbnails/6.jpg)
Sinusoids to Phasor Conversion
![Page 7: AC CIRCUITS ANALYSIS. Sinusoids A sinusoid is a signal that has the form of the sine or cosine function.](https://reader033.fdocuments.us/reader033/viewer/2022051014/55145bb4550346414e8b5642/html5/thumbnails/7.jpg)
Resistors in an AC Circuit
![Page 8: AC CIRCUITS ANALYSIS. Sinusoids A sinusoid is a signal that has the form of the sine or cosine function.](https://reader033.fdocuments.us/reader033/viewer/2022051014/55145bb4550346414e8b5642/html5/thumbnails/8.jpg)
Inductors in an AC Circuit
• The voltage leads the current by 90 degrees.
![Page 9: AC CIRCUITS ANALYSIS. Sinusoids A sinusoid is a signal that has the form of the sine or cosine function.](https://reader033.fdocuments.us/reader033/viewer/2022051014/55145bb4550346414e8b5642/html5/thumbnails/9.jpg)
Capacitors in an AC Circuit
• The current leads the voltage by 90 degrees.
![Page 10: AC CIRCUITS ANALYSIS. Sinusoids A sinusoid is a signal that has the form of the sine or cosine function.](https://reader033.fdocuments.us/reader033/viewer/2022051014/55145bb4550346414e8b5642/html5/thumbnails/10.jpg)
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).
![Page 11: AC CIRCUITS ANALYSIS. Sinusoids A sinusoid is a signal that has the form of the sine or cosine function.](https://reader033.fdocuments.us/reader033/viewer/2022051014/55145bb4550346414e8b5642/html5/thumbnails/11.jpg)
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).
![Page 12: AC CIRCUITS ANALYSIS. Sinusoids A sinusoid is a signal that has the form of the sine or cosine function.](https://reader033.fdocuments.us/reader033/viewer/2022051014/55145bb4550346414e8b5642/html5/thumbnails/12.jpg)
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.
![Page 14: AC CIRCUITS ANALYSIS. Sinusoids A sinusoid is a signal that has the form of the sine or cosine function.](https://reader033.fdocuments.us/reader033/viewer/2022051014/55145bb4550346414e8b5642/html5/thumbnails/14.jpg)
Problems4) Use mesh analysis to determine Vo.
ans: Vo = 12|_90° V
![Page 15: AC CIRCUITS ANALYSIS. Sinusoids A sinusoid is a signal that has the form of the sine or cosine function.](https://reader033.fdocuments.us/reader033/viewer/2022051014/55145bb4550346414e8b5642/html5/thumbnails/15.jpg)
Problems
5) Find Vx using nodal analysis.
ans:Vx =17.4|_-21.62°V