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Electrical Power

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…

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# Electrical Power

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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 ($\mathrm{W}$) and it is denoted by the symbol$P$. It is often measured in$\mathrm{kW}\left(1\mathrm{kW}=1000\mathrm{W}\right)$.

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 of$2-6\mathrm{W}$. This means that the charger draws$6\mathrm{W}$or$6$Joules per second from the mains. An electric kettle on the other hand has a power rating of$3\mathrm{kW}$. That is$3000$Joules per second which is$500$times the power consumed by the charger! This makes it$500$times 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:

$\mathrm{Power}=\mathrm{potential}\mathrm{difference}×\mathrm{current}$

where$P$is the electrical power,$V$is the potential difference across the component and$I$is the current passing through the component.

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

$P={I}^{2}R$

where$R$is the resistance of the electrical component.

Therefore,$1\mathrm{W}$of electric power can be defined as the energy transferred when a current of$1\mathrm{A}$flows through a potential difference of$1\mathrm{V}$.

## 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 $\left(\mathrm{J}/\mathrm{s}\right)$ which is the same the Watt $\left(\mathrm{W}\right)$.

$1\mathrm{J}/\mathrm{s}=1\mathrm{W}$.

As an example, imagine we have a lamp that requires a $12\mathrm{W}$incandescent lightbulb. The power rating of $12\mathrm{W}$ 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 $12\mathrm{J}$.

## 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, Vaia 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.

$P\mathit{=}I\mathit{×}R\mathit{×}I$

$P\mathit{=}{I}^{2}R$

or in words

$\mathrm{Power}={\left(\mathrm{Current}\right)}^{2}×\mathrm{Resistance}$

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

A$30\mathrm{\Omega }$appliance is supplied by a$3\mathrm{A}$supply, calculate the power rating of the speaker.

Step 1: List out the given quantities

$R=30\mathrm{Ώ}$, $I=3\mathrm{A}$

Step 2: Choose the right equation for calculating power

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

$P={I}^{2}R\phantom{\rule{0ex}{0ex}}P={\left(3\mathrm{A}\right)}^{2}×30\mathrm{\Omega }\phantom{\rule{0ex}{0ex}}P\mathit{=}270W$

So, the power consumed by the appliance is$270\mathrm{W}$.

Calculate the potential difference through an electric motor with a current of$10\mathrm{A}$and an electric power of$64\mathrm{W}$.

Step 1: List out the given quantities

$P=64\mathrm{W},\mathrm{I}=10\mathrm{A}$

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

$P=VI\phantom{\rule{0ex}{0ex}}V=\frac{P}{I}\phantom{\rule{0ex}{0ex}}V\mathbit{=}\frac{64\mathrm{W}}{10\mathrm{A}}=6.4\mathbit{}\mathrm{V}$

So the potential difference across the electric motor is$6.4\mathrm{V}$.

Calculate the power transferred when a current of$5\mathrm{A}$passes through a conductor of resistance$10\mathrm{\Omega }$.

Step 1: List out the given quantities

$\mathrm{R}=10\mathrm{\Omega },\mathrm{I}=5\mathrm{A}$

Step 2: Choose the right equation for calculating power

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

$P={I}^{2}R\phantom{\rule{0ex}{0ex}}P={\left(5\mathrm{A}\right)}^{2}×10\mathrm{\Omega }\phantom{\rule{0ex}{0ex}}P=250\mathrm{W}\phantom{\rule{0ex}{0ex}}$

The power is being transmitted is$250\mathrm{W}$.

## 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, Vaia

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 formula$P=VI$
• Electric power can also be calculated using the equation$P={I}^{2}R$
• 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.

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

The electric power dissipated in a circuit by a particular component can be calculated using the electric power formula: P=IV, where P is the power, V is the potential difference drop due to the component and I is the current passing through the component.

Electricity is generated in a power station by the combustion of fossil fuels. Water is heated until it reaches boiling temperature. The steam produced turns a turbine which powers a generator which produces electricity.

The SI unit of electric power is the Watt and it is denoted by the symbol W.

Consider any electrical appliance in your home, if it's using some electrical energy then it has a power output associated with it. Lightbulbs emit energy in the form of light and heat over a period of time, meaning they have a power rating.
If you're working on a laptop, you'll notice that the transformer on your laptop charger (the chunky cuboid part way along the cable) will have an input and output voltage and current. See if you can calculate the power input and power output of your laptop transformer!

## Electrical Power Quiz - Teste dein Wissen

Question

Power is directly proportional to the current flowing in the circuit.

True

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Question

1 Kilowatt =

1000 joules per second

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Question

What is the definition of power?

Power is defined as the rate of energy transfer per second

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Question

High voltage or high current, which of these can heat up a wire more?

High current

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