- #1
teng125
- 416
- 0
for i = 0.4A cos (wt + 60) , how do we get i(rt) =0.35A cos(wt + 30) and then i(ct) = 0.2A cos(wt+ 120) ??
A phasor is a complex number representation of a sinusoidal function. It is used to simplify the analysis of circuits or systems that involve AC signals, as it allows us to use algebraic operations instead of trigonometric functions.
To convert i(rt) and i(ct) from i(t) into phasor form, we use the Euler's formula: e^(jωt) = cos(ωt) + j sin(ωt). We can then rewrite i(rt) and i(ct) as I(rt) = I * e^(jωt) and I(ct) = I * e^(-jωt), respectively, where I is the peak amplitude of the current and ω is the angular frequency.
Using phasors allows us to represent sinusoidal signals as complex numbers, making it easier to perform algebraic operations and solve circuit problems. It also helps in visualizing and understanding the behavior of AC circuits.
No, phasors are only applicable for sinusoidal signals. For non-sinusoidal signals, we use Fourier series or Fourier transform to represent them in terms of sinusoidal components.
To convert phasors back into the time domain, we use the inverse Euler's formula: e^(jωt) = cos(ωt) + j sin(ωt). By multiplying the phasor by its complex conjugate, we can obtain the original sinusoidal function in the time domain.