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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:
<br /> \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}<br />
from where we can see that it is B=\frac{-X_L}{R^2+X_L^2},althought it is B=\frac{X_L}{R^2+X_L^2}.
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 B),the other is lowering(inductive reactance X_L) and vice-versa,like it is in Faraday`s law of induction:
e=-\frac{d\phi}{dt}
the magnetic field which is produced by induced current(which is in turn produced by induced electromotive force e) is in oposition with the change of outer flux \phi(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:
<br /> \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}<br />
from where we can see that it is B=\frac{-X_L}{R^2+X_L^2},althought it is B=\frac{X_L}{R^2+X_L^2}.
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 B),the other is lowering(inductive reactance X_L) and vice-versa,like it is in Faraday`s law of induction:
e=-\frac{d\phi}{dt}
the magnetic field which is produced by induced current(which is in turn produced by induced electromotive force e) is in oposition with the change of outer flux \phi(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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