for the past 3 yrs I have been trying to know y we use complex even though those imaginary sections could have been denoted by vectors.
such as for an LR circuit with voltage V,
I=V / (R i + X j) ...eq1 ..{i & j are vectors & V is also in vector}
instead of I=V/(R+jX) ...eq2
as the above was capable of working same as the later...
eq1=> V= IR i + IX j
eq2=> V= IR + j IX
in the same way for two || LR circuits with V.
I1 = V/ R1 i + X1 j & I2=V/R2 i +X2 j ;
I1 = V . (R1 i + X1 j) / {(R1 i + X1 j). (R1 i + X1 j)
= VR1 i + VX1 j / [{√( R1^2+ X1^2)}^2]
= {V/(√( R1^2 + X1^2))}.(sinψ i + cosψ j)
= I(sinψ i + cosψ j) where ψ = tan^(-1){R/X}
transforming the above into complex notation the same will be
= I e^(-jψ)
However when we proceed ahead we get a few anomalies ....
can any one explain all these mess to me????
such as for an LR circuit with voltage V,
I=V / (R i + X j) ...eq1 ..{i & j are vectors & V is also in vector}
instead of I=V/(R+jX) ...eq2
as the above was capable of working same as the later...
eq1=> V= IR i + IX j
eq2=> V= IR + j IX
in the same way for two || LR circuits with V.
I1 = V/ R1 i + X1 j & I2=V/R2 i +X2 j ;
I1 = V . (R1 i + X1 j) / {(R1 i + X1 j). (R1 i + X1 j)
= VR1 i + VX1 j / [{√( R1^2+ X1^2)}^2]
= {V/(√( R1^2 + X1^2))}.(sinψ i + cosψ j)
= I(sinψ i + cosψ j) where ψ = tan^(-1){R/X}
transforming the above into complex notation the same will be
= I e^(-jψ)
However when we proceed ahead we get a few anomalies ....
can any one explain all these mess to me????
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