# Watt’s the Deal with the Volt-Ampere?

## The commonly used volt-ampere gets easily confused with the watt when it comes to measurement in electrical systems design. So, watt exactly is the difference?

The volt-ampere is a commonly used but usually misconstrued measurement in electrical systems design. It is important to understand its proper usage when creating component specifications within a circuit.

Whenever we measure electrical power, we think about watts. The watt, named after the Scottish inventor James Watt, defines the power a system consumes. Specifically, electrical power is defined as the product of the system's instantaneous voltage input level and current consumption.

*Statue of James Watt, Birmingham, England. Image used courtesy of Adobe Stock*

Mathematically, the watt is defined as:

\[P(t)=V(t)^{*}I(t)[W]\text{ }(Eq. 1)\]

Here, P(t) is the system's electrical power in watts, while V(t) and I(t) are the system's voltage and current waveforms, respectively.

### The Difference Between Watt and Volt-Ampere

Interestingly, and often confusingly, there is another measurement with the same units as the watt, the volt-ampere (VA). As the name suggests, the units are the same as the watt, so what’s the difference between the two quantities? The difference is that while the watt defines the instantaneous power of an electrical system, the volt-ampere is defined as the product of the RMS voltage and the RMS current. This is also known as the apparent power and is formally defined as shown in Equation 2.

\[Apparent\,Power=V_{RMS}{^{*}}I_{RMS}[VA]\text{ }(Eq.2)\]

We can now see that the VA is not time-varying, but the watt is, and this is a crucial difference between the two. Furthermore, if we assume that V(t) and I(t) from equation 1 are sine waves of the form AV(t)sin(t+V) and AI(t)sin(t+I) respectively, the maximum RMS value of the instantaneous power, P(t), occurs when the two waveforms are in phase, and is equal to the apparent power. Thus, the VA, or apparent power, is the maximum power capacity of an electrical system, while the watt, or instantaneous power, is the amount of power actually used by the system, which is less than or equal to the apparent power value.

Now, we will more formally define the relationship between the VA and watt. Similar to impedance, power can have both real and imaginary components. Due to energy-storing components such as capacitors and inductors, an AC power supply's current and voltage waveforms tend to be out of phase. This means that the instantaneous power waveform of the system is less than it would be if it were completely in phase. This waveform represents the watt and is the real power that is actually supplied to the load. If the current and voltage waveforms were in phase, the instantaneous power waveform would be larger. This is the maximum power output of the AC power supply and is larger than when the current and voltage waveforms are out of phase, and this represents the apparent power measured in the volt-ampere (VA). Thus, we can illustrate the relationship between the real power, in watts, and the apparent power, in VA via the right triangle shown in Figure 1. Here, the vector difference between the two is the reactive power, unused power due to capacitance and inductance in the system, and measured in volt-amperes reactive (VAR).

**Figure 1. **Vector representations of real, apparent, and reactive power. Image used courtesy of Nick St. John

**Figure 1.**Vector representations of real, apparent, and reactive power. Image used courtesy of Nick St. John

Another way to illustrate the relationship between the VA and the watt is by thinking of a glass of beer, as seen in Figure 2. Here, the total volume of the glass represents the apparent power (VA) and is the system demand, meaning the power being delivered by the power supply. Next, the beer represents the real power (W) being delivered to the power supply load (the system being powered). Lastly, the unusable part, the foam, represents the reactive power (VAR) and is any power from the supply that does not get used and instead generates heat or vibrations.

**Figure 2. **Analogy of types of power measurements compared to a glass of beer with foam. Image used courtesy of EEPower

**Figure 2.**Analogy of types of power measurements compared to a glass of beer with foam. Image used courtesy of EEPower

Now that we have discussed the difference between the two values, what is the significance of both of these quantities? When a power supply delivers power to a load, the watt defines the amount of power the load uses, while the VA defines the total power the power supply expends. Together, these two values can allow one to measure how efficient an entire system is. Ideally, we want all power put out by the supply to be taken up by the load, but, in reality, this is not the case. Thus, we define the power efficiency of the system as the Power Factor (PF), which is the ratio of the real power vs the apparent power:

\[PF=\frac{Real\,Power(W)}{Apparent\,Power(VA)}\text{ }(Eq.3)\]

For an electrical load with purely real impedance (a resistor), the power factor would be 1.0, as the load takes all power dissipated by the power supply. Meanwhile, the power factor is zero if the load is purely reactive (a capacitor or inductor). Here, since the current and voltage waveforms are completely out of phase, half of the signal period will have the power supply supplying power to the load, while in the second half, the load will supply the power back to the power supply. These cancel each other out, and, in reality, the system dissipates no real power; therefore, the power factor is zero.

### Volt-Amperes in System Design

Besides measuring system efficiency, what else can the VA be used for? When designing a system, an engineer must ensure reliability, meaning the wires and components must withstand whatever voltages and currents are seen. How is this done? Let’s say we are designing a simple circuit to power a light via a switch from a 120-V plug in a home, as shown in Figure 3.

**Figure 3. **Circuit to power a lightbulb from a 120 V source. Image used courtesy of Nick St. John

**Figure 3.**Circuit to power a lightbulb from a 120 V source. Image used courtesy of Nick St. John

If the lightbulb is rated for 100 VA (in reality, VA or watts will be used as the rating), this is the maximum power allowed across the lightbulb. Since we know the light will be powered via a 120 V source, the maximum RMS current can be calculated as 100/120=0.83 A. As designers, we now know the maximum current allowed through the system is 0.83 A, and we can size the wires and power switch to allow a current of that magnitude. We can install a fuse before the switch that will blow if the current exceeds this maximum value, protecting the lightbulb from overloading.

Another example of how the VA can be helpful is if our 120 V source is a designed power supply rather than a house plug. Here, the VA allows us to calculate the same current as before, defining the maximum current output the power supply needs to supply this load reliably. Thus, we can see that the VA allows us to determine the specifications for power supplies and size wires, circuit breakers, and fuses to guarantee that the designed electrical system will operate reliably and safely at all times.

Watts and volt-amperes are commonly used in electrical system design but are just as commonly confused, so it is important to understand their proper use when creating component specifications within a circuit.

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