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Why is inductive reactive power considered positive while capacitive reactive power is considered negative in the circuit ?

Both inductor and capacitor consume apparent power so I guess total reactive power in the circuit should be written as.

Total reactive power = Total inductive reactive power + Total capacitive reactive power.

but in books it is

Total reactive power = Total inductive reactive power - Total capacitive reactive power.Is this because energy oscillates between the inducter and the capacitor?

I do not understand this. Can anyone help me on this ?

Could you say why the sign is negative for Capacitor whereas this also store energy inform of charges and Inductor also stores energy in magnetic form. Then why Capacitor -ve and Inductor is Positive ??

Anyone can give a good analogy to understand this concept ?

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3 Answers 3

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'Both inductor and capacitor absorb power' - NO

They both store energy (the integral of power).

In an AC circuit, a simple one where there's only one capacitor and one inductor, doesn't matter whether series or parallel connection, one will be accumulating energy while the other is discharging energy. One will be taking power, the other will be generating power.

The net change in total energy storage seen at the terminals will be the algebraic sum of the changes at the L and at the C. As one is the opposite sign to the other, the sum is the difference in their magnitudes.

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  • \$\begingroup\$ Could you say why the sign is negative for Capacitor whereas this also store energy inform of charges and Inductor also stores energy in magnetic form. Then why Capacitoy -ve and Inductor is Positive ?? \$\endgroup\$
    – Photon001
    Jan 19, 2016 at 9:49
  • \$\begingroup\$ I didn't say the sign is -ve for capacitor, I said the signs are opposite for inductor and capacitor. I don't like arbitrary conventions where one is -ve and the other positive, but conventions are necessary to communicate via formula with the rest of the scientific community. However, for gut level understanding, you only need to know they're different. Why are they different? I in cap is dV/dt, V in inductor is dI/dt, so for a sinusoidal V and I waveform, one leads in quadrature, the other lags, so they end up 180 degrees in phase from each other. Marko Bursic's spring comment is good! \$\endgroup\$
    – Neil_UK
    Jan 19, 2016 at 10:44
  • \$\begingroup\$ @user44635 can you please tell that if RLC is connected with an Ac source then the energy stored by L and C will again cancel each other ? will then also one will be accumulating energy while the other will discharging energy. \$\endgroup\$ Jan 22, 2016 at 21:33
  • \$\begingroup\$ @hurchuchu they will only cancel when the AC frequency is equal to their resonant frequency, and one will be discahrging while the other is accumulating. At other frequencies, the rate of change of energy at each will not be equal, they won't cancel, but their effective sum will be less than the larger of the two. \$\endgroup\$
    – Neil_UK
    Jan 22, 2016 at 21:42
  • \$\begingroup\$ @user44635 in steady state RLC circuit with ac source still they calculate net reactive power as the difference of inductive and capacitive reactive power. why is that ? \$\endgroup\$ Jan 22, 2016 at 21:58
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The best example I can think of is a capacitor in parallel with an inductor fed from an AC voltage source of a very specific frequency. When the frequency is chosen so that the magnitudes of the reactances are equal, there is zero net power delivered by the AC voltage source.

This is also known as a parallel tuned circuit and it is well-known for producing infinite impedance at resonance. Infinite impedance means no power can be delivered to it and it takes zero current. Here is an example: -

enter image description here

At slightly below resonance there is a small amount of current and slightly above resonance there is a small amount of current but, at resonance there is zero current because the current flow in the capacitor is 180 degrees opposite to the current flow in an inductor and, when those two currents are equal in magnitude, the net current is zero.

This has to mean an A minus B relationship and not an A plus B relationship.

Another example is the series resonant LC circuit. At series resonance, impedance is zero because the impedances of L and C are equal in magnitude but opposite in value. Because series impedances add, any two values that "add" but potentially produce "zero" MUST mean that the inductive reactance has an opposite "sign" to the capacitive reactance.

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Because it has imaginary part, apparent power (S) is a vector sum of real power (P) and reactive power (Q). S=P+jQ. Inductive reactance has positive imaginary sign Xl=jwL, while the capacitive reactance has negative sign Xc=-j/wC. If both reactances are equal, then they cancell each other.

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  • \$\begingroup\$ This is Mathematical form, Anyone can give a good analogy to understand this concept ? \$\endgroup\$
    – Photon001
    Jan 19, 2016 at 9:50
  • \$\begingroup\$ Let's say you have a spring and mass. If you strech the spring you give the initial energy into the spring, then you relaese the spring will push the mass. You have the conversion from elastic energy into kinetic enegy, back and forth all the time. Those are those reactive energies, you can give a negative/positive sign wherever you want, important is that they are different for elastic energy and for kinetic energy as they continously bounce. \$\endgroup\$ Jan 19, 2016 at 9:57

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