How do you calculate reactive power in an AC circuit?

Inductive Load:

For an inductive load, the reactive power (Q) can be calculated using the following formula:

Q = Vrms * Irms * sin(θ)

Where:

Vrms is the root-mean-square (RMS) voltage across the inductor (in volts).

Irms is the root-mean-square (RMS) current flowing through the inductor (in amperes).

θ is the phase angle difference between the voltage and current. In an inductive circuit, the current lags behind the voltage by an angle θ, typically denoted as the power factor angle (φ). So, θ = φ.

Capacitive Load:

For a capacitive load, the reactive power (Q) can be calculated using the following formula:

Q = Vrms * Irms * sin(θ)

Where:

Vrms is the root-mean-square (RMS) voltage across the capacitor (in volts).

Irms is the root-mean-square (RMS) current flowing through the capacitor (in amperes).

θ is the phase angle difference between the voltage and current. In a capacitive circuit, the current leads the voltage by an angle θ, which is the power factor angle (φ). So, θ = -φ (negative because the current leads the voltage).

For both inductive and capacitive loads, the reactive power Q is positive, indicating that it is being absorbed by the load.

If you know the capacitance (C) and inductance (L) values of the load, you can also use angular frequency (ω) to calculate reactive power:

For capacitive load: Q = Vrms * Irms / ωC

For inductive load: Q = Vrms * Irms * ωL

Remember that reactive power does not represent actual power consumed by the load but instead represents the power required to establish the magnetic or electric fields in the inductor or capacitor, respectively. Actual power consumed in the circuit is called active power, and the combination of active and reactive power is called apparent power. Apparent power is calculated as the vector sum of active power (P) and reactive power (Q):

Apparent power (S) = √(P^2 + Q^2)