# Reactive power equation

Discussion in 'General Electronics Chat' started by Moxica23, Jun 23, 2014.

1. ### Moxica23 Thread Starter New Member

Jun 23, 2014
12
1
Hi,

Here it says that the equation for Reactive power is

$Q=\frac{E^2}{X}$

but in many other places I found that the correct equation is:

$Q=\frac{E^2}{X}*sin phi$

where "phi" is the phase delay between current and voltage.

So, which is the correct version of that equation ?

Regards

2. ### crutschow Expert

Mar 14, 2008
13,496
3,373
The first equation is correct if X is just a reactive impedance.
The second equation is correct for X being any impedance (often indicated by the complex number Z).

3. ### Moxica23 Thread Starter New Member

Jun 23, 2014
12
1
So the first equation describe the situation when in that circuit we have only reactance (capacitive or/and inductive) and no resistance ?

And the second equation describe the situation when in our circuit we have both reactance and inductance ?

If so, why the first equation is included in the calculation methodology for power factor corection for the case when in our circuit we have an electric motor ? An electric motor have both rectance and resistance. They shouldn't use the second equation ?

4. ### crutschow Expert

Mar 14, 2008
13,496
3,373
If the measured voltage is directly across the reactance and not the complete circuit than the first equation works.

5. ### Moxica23 Thread Starter New Member

Jun 23, 2014
12
1
Yes, I agree. But on this page they speak about a circuit in which an electric motor is the only load. Considering that an electric motor has also some electric resistance, I ask myself why they used the equation for the case when the load is only a reactance.

6. ### MrAl Distinguished Member

Jun 17, 2014
2,554
515
Hi,

Could that be because they just want to calculate the reactive power, not the total power?

7. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
783
The OP's link to the AAC page reveals this is in relation to power factor correction (pfc).

The object is to achieve a load side unity power factor. The value of Q as shown in that case is the leading compensation VARS required from a pfc capacitor placed in parallel with a lagging power factor load connected to a supply E. Since a pure capacitance exhibits a 90° phase shift in its current and applied terminal voltage, the sin(phi) value is unity.

I'm also querying the supposedly "correct" equation

$Q=\frac{E^2}{X}sin(\phi)$

I would rather have

$Q=\frac{E^2}{|Z|}sin(\phi)$

where E is the voltage applied to a general impedance Z = R±jX and

$|Z|=\sqrt{R^2+X^2}$

$\phi=\mp \arctan(\frac{X}{R})$

Last edited: Jun 24, 2014
Moxica23 likes this.