Sinusoidal Source
A sinusoidal current is usually referred to as alternating current (ac). Circuits driven by sinusoidal current or voltage sources are called ac circuits.
(a)A sinusoidal signal is easy to generate and transmit. It is the dominant form of signal in electric power industries and communication.
(b) Nature itself is characteristically sinusoidal.
(c) Through Fourier analysis, any practical periodic signal cab be represented by a sum of sinusoids.
(d) A sinusoid is easy to handle mathematically. The derivative and integral of a sinusoid are themselves sinusoids.
Vm : the amplitude of the sinusoid
ω : the angular frequency , rad/s
θ : phase angle , rad
ω =2πf
f : frequency , Hz
T=1/f=2π/ω
Phasors
A phasor is a complex number that represents the amplitude and phase of a sinusoid. Introduced by Charles Proteus Steinmetz, a German-Austrian mathematician and engineer, in 1893. The idea of phasor representation is based on Euler’s identity :
A convention used in power systems is as follows:The electric load is lagging, which means the load current phasor lags the voltage phasor.
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 Ω. It is a frequency-dependent quantity.
It represents the opposition that the circuit exhibits to the flow of sinusoidal current.
where R = Re Z is the resistance and X = Im Z is the reactance.
The admittance Y is the reciprocal of impedance, measured in siemens (S).
where G = Re Y is the conductance and B = Im Y is the susceptance.
Z=R− Jx capacitive/leading (I leads V)
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