# Units and Dimensions

Recently I came across a question where they have asked which of the options is a unit of power. It had both kVA and kW in options. My teacher told me that the former is used as per rating ( neglecting the power factor) and latter is used for actual power.

This had me confused. Aren't they both the same? Is this similar to the case where we say joules is unit of energy but not torque. So when two units have same dimensions, do we have to follow a convention to use them?

Wikipedia says kWH is a derived UNIT of energy. Now, is it based solely on the fact that they have same dimensions or is it because it is commonly used and thus, accepted. Would it be alright if I refer to unit of force as $\operatorname{kg} \operatorname{m}/\operatorname{s}^2$?

For ac power as well as the watt (W) for real (or active) power electrical engineers use the volt-amp (VA) for apparent power and volt-amp-reactive (VAR).for reactive power.

For a purely resistive circuit real power and apparant power are the same and reactive power is zero.

For a circuit which has both resistance and reactance there will be a phase difference $\phi$ between the applied voltage and the current.

In such a circuit if you measured the rms value of applied voltage $V$ and the rms value of the current $I$ and multiplied the two quantities together you would get the apparent power $VI$ measured in $VA$.

Real power is a measure of the power supplied to the circuit by the power supply which does not come back to the power supply.
This power ends up as heat in the resistive parts of a circuit or used by motors to do work.
Real power $=VI \cos \phi$ where $\cos \phi$ is called the power factor of the circuit and this quantity is measured in watts.
If a circuit is purely inductive or purely capacitive then the phase angle between current and voltage is $\frac \pi 2$, $\cos \theta = 0$ and the real power is zero. However that is not to say that there is no current flowing in the circuit.
During a cycle reactive components are supplied electrical power during one half of a cycle and then return the electrical power during the other half of the cycle.
The net electrical power dissipated by a reactive component is zero.

The amount of power going backwards and forwards between the circuit and the power supply is important and it is called the reactive power $(=VI \sin \phi)$ and has the unit VAR.

The relationship between the tree types of power is

$\rm power_{apparent}^2 = \rm power_{real}^2 + \rm power_{reactive}^2$

kWh is the kilowatt-hour and is a unit of energy.
It is the energy used by a device in one hour during which the power supplied to the device is one kilowatt.

$\rm 1\,kWh = 1000 \times 60 \times 60 = 3\,600\,000 \,J$

If you ever look at the adapter of a electrical device, perhaps one of your printer or laptop's charger, you'll notice it has both the quantities written on it, one in kVA and one in kW. Moreover, the value in kW will always be a fraction(less than 1) of the value in kVA.
The value in kVA is basically the power supplied and the one in kW is the power which is used out of the power supplied.
For example, in a 600VA/360kW battery for every 600W of power supplied it stores 360W worth. Mathematically these units may seem same but have different interpretations