The electric power is the rate at which a system delivers, consumes, or transforms electrical energy.
We already know that voltage pushes and resistance holds back. The result is the movement of electrons (current).
But what is all this for? To do something useful. To transform that electricity into something else: motion (motors), light (LEDs), or heat (ovens).
That is why we need two quantities that define the “rate” and the “amount” of our system: power and energy. They are often confused, but they are very different things. Let’s see this clearly.
Electric Power (P)
Power is the rate at which energy is transferred or transformed. It tells us how much energy changes form each second.
Its unit in the International System is the watt (W).
Mathematically, in direct current (DC), power is the product of voltage and current:
The relationship is simple:
- If we have a lot of force (V) and a lot of flow (I), we have a lot of power (P).
Car analogy:
- Power (W) is the speed you are going (km/h).
- Energy (J) will be the distance you have traveled at the end of the trip (km).
You can have a very powerful car (many W), but if you don’t turn it on, you consume no energy.
Joule’s Law: The Price of Resistance
Now let’s combine the power formula (P = V · I) with Ohm’s Law (V = I · R). If we substitute V, we obtain one of the most important formulas in engineering, the Joule’s Law:
This formula tells us something important: the dissipated power depends on the square of the current.
This has brutal consequences:
- If you double the current (x2), the heat generated is multiplied by four (x4).
- If you triple the current (x3), the heat is multiplied by nine (x9).
This is why overloading an electrical line is so dangerous. A small increase in current can cause the cable temperature to skyrocket and start a fire.
Where does that power go?
In an ideal resistor, all the absorbed electrical power is transformed into heat.
- In a heater, this is great. It’s what we want.
- In a computer or a motor, this is a loss. It is wasted energy that also forces us to use fans to prevent the equipment from melting.
Electric Energy (E)
If Power is the speed, Energy is the total amount of work done over a given time.
The International System unit is the joule (J), which is equivalent to 1 watt for 1 second
This relationship is very important: energy always appears when power acts over a certain time. Without time, there is no accumulated energy, only the instantaneous capacity to do work.
Why we use the kWh
The joule is a very small unit for everyday consumption. If you turn on a 1000 W heater for one hour, it will have transformed:
Expressing household consumption in millions of joules would be awkward. That’s why we use a more practical derived unit: the kilowatt-hour (kWh).
How to calculate what you will pay?
The calculation is very simple and important for any engineering or domestic project:
- Look at the power of your appliance in watts (W) and convert it to kilowatts (kW) by dividing by 1000.
- Estimate how many hours (h) it will be on.
- Multiply.
Example:
- You have a gaming computer that consumes 500 W at full performance.
- You play for 4 hours.
Assuming a price of €0.15/kWh, that gaming session costs:
Important note: kW/h is not the correct unit to express electrical consumption. The correct one is kWh, which is a unit of energy.
Summary of Magnitudes
At this point, we have the complete dashboard. Let’s organize it to avoid getting lost:
| Magnitude | Symbol | Unit | Concept | Key Formula |
|---|---|---|---|---|
| Voltage | V | Volt (V) | Energy per charge (Pressure) | |
| Current | I | Ampere (A) | Charge per second (Flow) | |
| Resistance | R | Ohm (Ω) | Opposition to flow | |
| Power | P | Watt (W) | Rate of work | |
| Energy | E | J (or kWh) | Total accumulated work |
