Capacitor/Inductor Imaginary Numbers

[Adder_Noir]

Dear All,

Why do we introduce complex numbers when talking about the voltage behaviour through capacitors and inductors. Any help would be appreciated,

Thanks

 

[Mr Jake]

because the components induce a 90 degree phase shift between the voltage and current signal, J simply represents a 90 degree phase shift.
for example is a sin wave was aplpied to a capacitor then the voltage would be V=Va*Sin(a) whereas the current would follow I = Ia*Sin(a + 90).
when analysing filters with reactive components the complex and real parts of the transfer function help to find the magnitude and phase at various frequencies.

 

[Gokul43201]

Simply put, it takes 2 numbers to specify the instantaneous value of an AC signal. You can use the vactor/phasor representation, and specify amplitude and phase, or you can use the complex notation and specify real and imaginary components. The two systems are alternative representations of the same idea, and you can easily switch from one to the other.

 

[Antiphon]

Complex numbers are an easy way to manipulate equations which
involve periodic signals, like sin(wt).

Because exp(jwt) = sin(wt) + jcos(wt), you can work with the
amplitude and phase in a single convenient function.