Electrical Power: Definition, Formula & Unit | StudySmarter

Electrical power runs the world around us. Thanks to Nikola Tesla’s discovery of alternating current (AC) power, homes all around the world receive Electricity. So then what exactly does electrical power have to do with the electricity that powers our appliances? This article will give you a detailed explanation of the definition of power, its equations, and its properties. We will also study the relationship between power, current, voltage, and other quantities. Happy learning!

Electrical Power Definition

Electrical power arises from the flow of charge, known as current, due to the electrical energy arising from a potential difference.

Electric power is defined as the electrical energy transferred in a circuit per unit of time.

The unit of electric power is the Watt (W) and it is denoted by the symbolP. It is often measured inkW (1 kW = 1000 W).

The power rating that we see in our home appliances defines how much energy is being transferred from the grid to power the device. A mobile phone charger has a power rating in the range of2 – 6 W. This means that the charger draws6 Wor6Joules per second from the mains. An electric kettle on the other hand has a power rating of3kW. That is3000Joules per second which is500times the power consumed by the charger! This makes it500times more expensive to use than your typical mobile charger. Let us now look at how to calculate the power using the current drawn and the voltage.

Factors of electrical power

The electrical power used by an electrical component depends on two main factors. These factors are:

• The current I passing through the component.
• The potential difference/voltage V across the two ends of the component

increasing either one of these variables will increase the power proportionally. This can be formulated as an equation for power in terms of these two variables which we demonstrate in the next section of this explanation.

Electrical power formula

The electric power transferred to an electrical component in a circuit can be calculated using the electric power formula:

P=VI

Or in words:

Power=potential difference×current

wherePis the electrical power,Vis the potential difference across the component andIis the current passing through the component.

The electric power can also be calculated by knowing the current and resistance using the following equation

P=I2R

whereRis the resistance of the electrical component.

Therefore,1 Wof electric power can be defined as the energy transferred when a current of1 Aflows through a potential difference of1 V.

Unit of electrical power

The units of electrical power, like all other forms of power, is Watts \(W\) or often kilowatts \(kW\). Power is a measure of the time rate at which energy is transferred to or from an object or more generally some physical system. Therefore electrical power can also have units of Joules per second (J/s) which is the same the Watt (W).

1 J/s = 1 W.

As an example, imagine we have a lamp that requires a 12 W incandescent lightbulb. The power rating of 12 W indicates that the total energy used by the lightbulb in one second, in the form of both light energy and wasted thermal energy, is equal to 12 J.

Electrical power triangle

The electric power triangle is an easy way to memorize the above equation. This formula can be rearranged with the help of an Electrical power triangle shown below.

Electrical Power Electric Power triangle, StudySmarter Originals

We can derive the second electrical power formula using Ohm’s law. The equation for Ohm’s law is given by

V=IR

We can substitute the value for the potential difference into the equation for power.

P=I×R×I

P=I2R

or in words

Power=(Current)2×Resistance

Let us look at a few examples where we calculate power:

A30 Ωappliance is supplied by a3 Asupply, calculate the power rating of the speaker.

Step 1: List out the given quantities

R=30 Ώ, I=3 A

Step 2: Choose the right equation for calculating power

We have the values for current and resistance we can use the following equation

P=I2RP=(3 A)2 × 30 ΩP=270 W

So, the power consumed by the appliance is270 W.

Calculate the potential difference through an electric motor with a current of10 Aand an electric power of64 W.

Step 1: List out the given quantities

P=64 W, I = 10 A

Step 2: Choose the right equation for calculating the potential difference

We have the values for current and resistance, we can use the following equation

P=VIV=PIV=64 W10 A=6.4 V

So the potential difference across the electric motor is6.4 V.

Calculate the power transferred when a current of5 Apasses through a conductor of resistance10 Ω.

Step 1: List out the given quantities

R = 10 Ω, I= 5 A

Step 2: Choose the right equation for calculating power

We have the values for current and resistance we can use the following equation

P=I2RP=(5 A)2×10 ΩP=250 W

The power is being transmitted is250 W.

Power transmission

For a given value of current, the power consumed increases with an increase in potential difference. The magnitude of power consumed depends on both the current and the potential difference. Therefore electric power can be delivered in the same quantity using different combinations of potential difference and current.

• Low current with a high voltage
• High current with a low voltage

Warning signs outside power stations indicate that the voltages present are dangerous to humans and could cause serious harm in the form of an electric shock, StudySmarter

The disadvantage of using a high current with a low potential difference is the heating effect. When large values of current pass through a wire they heat up to high temperatures which reduces the lifetime of the wires. The heating effect is bad as it reduces the efficiency of the electric device. This is because a part of the energy that is being transferred is being converted into heat. For this reason, High powers across the mains are transmitted in high voltages with low currents.

The heating effect is due to the current passing through a resistor. The heat produced is directly proportional to the resistance of the wire or device. When current passes through a conductor it overcomes the resistance of the wire, the work done against the resistance is converted into heat.

Electrical Power – Key takeaways

• Electric power is defined as the electrical energy transferred in a circuit per unit of time.
• Electric power or the electric energy transferred in a circuit can be calculated using the electric power formulaP=VI
• Electric power can also be calculated using the equationP=I2R
• The disadvantage of using a high magnitude of current with a low voltage is the heating effect. When large values of current pass through a wire they heat up to high temperatures which reduces the life of the wires leading to high maintenance costs and wasted energy.
• High powers across the mains are transmitted in high voltages with low currents.