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Usually the capacitive reactance in a a circuit is represent in phasor form as X(c)= |X(c)|\$\angle 90\$.

If we convert this phasor expression to sinusoidal expression we get. X(c)= |X(c)|sin(wt-90).

Does this mean that capacitive reactance is also time changing ?

If that is the case then at t=0 we get.

X(c) = |Xc|sin(0-90) = -|Xc|. so at t=0 we are getting negative reactance. I really do not understand how reactance can be negative.

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  • \$\begingroup\$ What does "X(c)= /X(c)/<90 degree" mean? I don't understand the forward slashes (/) and what they mathematically represent. Do you mean "|" as used either side of a variable to represent magnitude? If you do then does the "<" symbol mean "angle"? What about using mathjax i.e. \$\angle{90}\$. \$\endgroup\$
    – Andy aka
    Commented Sep 29, 2016 at 11:00
  • \$\begingroup\$ yes /X(c)/ is the magnitude and <90 degree is the angle of the phasor. \$\endgroup\$
    – Alex
    Commented Sep 29, 2016 at 11:01
  • \$\begingroup\$ How components store sinusoidal energy by lagging or leading current by 90deg determines the phasor polarity of the reactive impedance. When an equal + and - reactive impedance are together they cancel out ( at one frequency ) The magnitudes are usually stated in VAR's for grid parts and Z(f)= R+jX(f) in this domain \$\endgroup\$
    – D.A.S.
    Commented Sep 29, 2016 at 11:02
  • \$\begingroup\$ I've edited it but you better take a CAREFUL look to see it still represents what you originally meant it to \$\endgroup\$
    – Andy aka
    Commented Sep 29, 2016 at 11:04
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    \$\begingroup\$ Voltage and current are phasors (well, can be represented as such). The reactance is just a complex number that tell you how their amplitude and phases are related. There is no 'conversion to sinusoidal expression' for X. \$\endgroup\$
    – Sredni Vashtar
    Commented Sep 29, 2016 at 18:25

1 Answer 1

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Look at the current for an inductor and the current for a capacitor when applied the same sine wave voltage: -

enter image description here

Clearly the capacitor current and inductor current are 180 degrees apart. Clearly they also both have equal magnitudes of reactance when operating at this frequency with those values of C and L.

This means that if one reactance is positive then the other has to be negative.

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  • \$\begingroup\$ is reactance also time changing or its constant. someone claims "For an ideal capacitor or inductor reactance remains the same with varying voltage since the current changes when you change the voltage. " while other claims. "The current through a capacitor always leads the resulting Voltage across the capacitor by 90 degrees which is one fourth of a cycle. Thus the instantaneous reactance [(instantaneous Vc)/(instantaneous Ic)] of a capacitor is constantly changing during each cycle of an ac sine wave Voltage that is applied to a capacitor. @andy aka \$\endgroup\$
    – Alex
    Commented Sep 30, 2016 at 6:51
  • \$\begingroup\$ Clearly, on the face of it dividing instantaneous sine by cos appears to equal tan and as an impedance that looks a total mess. It works for a resistor of course but that's just one case. Reactive or any complex impedance uses rotating vectors (or phasors) to resolve what seems to be the anomaly. \$\endgroup\$
    – Andy aka
    Commented Sep 30, 2016 at 7:13
  • \$\begingroup\$ really id didnt understand much what you said. can you please explain ? i just need to know that whether reactance is time changing or its constant in an ideal inductor or capacitor ? not much is clearly written on this in my book. \$\endgroup\$
    – Alex
    Commented Sep 30, 2016 at 7:27
  • \$\begingroup\$ Reactance is constant by definition providing that the RMS current and RMS voltage rise and fall together (not the instantaneous values) and that any phase difference between current and voltage is also constant: electronics-tutorials.ws/accircuits/ac-inductance.html \$\endgroup\$
    – Andy aka
    Commented Sep 30, 2016 at 7:34
  • \$\begingroup\$ thanks alot. are you on face book ? may i add you please? @andy aka \$\endgroup\$
    – Alex
    Commented Sep 30, 2016 at 7:38

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