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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{RjX_L}{RjX_L}=\frac{RjX_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 viceversa,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.
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{RjX_L}{RjX_L}=\frac{RjX_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 viceversa,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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