Ece Tutorial 2 - Phasors

Ece Tutorial 2 - Phasors - What you always wanted to know...

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Sheet1 Page 1 What you always wanted to know about PHASORS and IMPEDANCES but were afraid to ask We have learned that the voltage across an inductor is proportional to the time derivative of the current through the inducto There is, however, one very important special case when differential equations can be replaced by complex analysis. This i s V(t) = Vp cos (w t + q v) for voltages and i(t) = ip cos (w t +q i) By definition, any complex number Z is represented as Z = Re{Z} + j Im{Z} (rectangular form), or Z = M (cos a + j sin a) (polar form) where j = sqrt(-1), Re{Z} is the real part and Im{Z} is the imaginary part of the complex number Z, M is its magnitude, and a is t h exp (j a) = cos a + j sin a It follows from here that the polar form of any complex number can be represented as Z = M exp (j a) and our functions can be rewritten as real parts of complex numbers: V(t) = Re{Vp exp[j (w t + q v)]} and i(t) = Re{ip exp[j (w t +q i)]} Let us rewrite our functions once again: V(t) = Re{Vp exp (jq v) exp (jwt)} = Re{V exp (jw t )} and i(t) = Re{ip exp(jqi) exp (jwt)} = Re{i exp (jw t )} where V = Vp exp (jq v)
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Ece Tutorial 2 - Phasors - What you always wanted to know...

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