Reactive Power in the circuit

Question

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 ?

Answer 1

'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.

Answer 2

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: -

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.

Answer 3

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.