If the complex power is 1,500 VA with a power factor of 0.866 lagging, what is the reactive power (VAR)?

To determine the reactive power in VAR, you can start by using the relationship between complex power (S), real power (P), and reactive power (Q) in AC circuits. The complex power S is expressed as:

[ S = P + jQ ]

where:

• S is the complex power in VA,

• P is the real power in watts (W), and

• Q is the reactive power in volt-amperes reactive (VAR).

Given that the complex power S is 1,500 VA and the power factor is 0.866 lagging, the real power P can be calculated using the power factor (PF):

[ P = S \times \text{PF} ]

Substituting the known values:

[ P = 1500 , \text{VA} \times 0.866 = 1299 , \text{W} ]

Next, to find the reactive power Q, you can use the following relationship derived from the Pythagorean theorem in the context of power in an AC circuit:

[ |S|^2 = P^2 + Q^2 ]

Rearranging gives:

[ Q = \sqrt{|S|^2 - P^2