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

AC CIRCUITS ANALYSIS

Sinusoids

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

Phasors

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

Phasors

Phasors

Sinusoids to Phasor Conversion

Resistors in an AC Circuit

Inductors in an AC Circuit

• The voltage leads the current by 90 degrees.

Capacitors in an AC Circuit

• The current leads the voltage by 90 degrees.

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).

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).

Problems

1)

2)

Problems

3) Determine the input impedance of the circuit at ω = 10 rad/s.

Answer: 32.38 − j 73.76 ohms.

Problems4) Use mesh analysis to determine Vo.

ans: Vo = 12|_90° V

Problems

5) Find Vx using nodal analysis.

ans:Vx =17.4|_-21.62°V