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Suppose that we have a simple system like one illustrated in attachment.

If we need to find complex admittance of that system,we can write:

[tex]

\underline{Y}=G+jB=\frac{1}{\underline{Z}}=\frac{1 }{R+jX_L}\cdot\frac{R-jX_L}{R-jX_L}=\frac{R-jX_L}{R^2+X_L^2}=\frac{R}{R^2+X_L^2}+j\frac{-X_L}{R^2+X_L^2}

[/tex]

from where we can see that it is [tex]B=\frac{-X_L}{R^2+X_L^2}[/tex],althought it is [tex]B=\frac{X_L}{R^2+X_L^2}[/tex].

Why is this "-" just neglected,what is physical explanation of that?

Or it is just hardcore mathematical laws against imperfect physical reality?

Also,is it because complex numbers are just,let`s say it like this,"artificial" extension of real numbers set?

Probably the explanation is that while one physical parameter is rising(susceptance [tex]B[/tex]),the other is lowering(inductive reactance [tex]X_L[/tex]) and vice-versa,like it is in

[tex]e=-\frac{d\phi}{dt}[/tex]

the magnetic field which is produced by induced current(which is in turn produced by induced electromotive force [tex]e[/tex]) is in oposition with the change of outer flux [tex]\phi[/tex](sorry if my technical english sounds a bit clumsy).

But what if there is capacitor instead of inductor?

In that case there is no confusion like this.

There is also a "-" when active and reactive power for system like one illustrated in attachment is calculated.

If we need to find complex admittance of that system,we can write:

[tex]

\underline{Y}=G+jB=\frac{1}{\underline{Z}}=\frac{1 }{R+jX_L}\cdot\frac{R-jX_L}{R-jX_L}=\frac{R-jX_L}{R^2+X_L^2}=\frac{R}{R^2+X_L^2}+j\frac{-X_L}{R^2+X_L^2}

[/tex]

from where we can see that it is [tex]B=\frac{-X_L}{R^2+X_L^2}[/tex],althought it is [tex]B=\frac{X_L}{R^2+X_L^2}[/tex].

Why is this "-" just neglected,what is physical explanation of that?

Or it is just hardcore mathematical laws against imperfect physical reality?

Also,is it because complex numbers are just,let`s say it like this,"artificial" extension of real numbers set?

Probably the explanation is that while one physical parameter is rising(susceptance [tex]B[/tex]),the other is lowering(inductive reactance [tex]X_L[/tex]) and vice-versa,like it is in

*Faraday`s law of induction*:[tex]e=-\frac{d\phi}{dt}[/tex]

the magnetic field which is produced by induced current(which is in turn produced by induced electromotive force [tex]e[/tex]) is in oposition with the change of outer flux [tex]\phi[/tex](sorry if my technical english sounds a bit clumsy).

But what if there is capacitor instead of inductor?

In that case there is no confusion like this.

There is also a "-" when active and reactive power for system like one illustrated in attachment is calculated.

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