Electric Power and Electrical Energy

Introduction to Electric Power

Electric power is the rate at which electrical energy is transferred, converted, or consumed in an electrical circuit.

Electrical energy may be:

• Supplied by a battery or power source
• Converted into heat by a resistor
• Converted into light by a bulb
• Converted into mechanical energy by a motor

The SI unit of electric power is the watt (W).

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Joule’s Heating Effect

James Prescott Joule (1818–1889) studied the heating effect produced when electric current flows through a conductor.

According to Joule’s Law of Heating, the heat produced in a conductor is:

• Directly proportional to the square of current
• Directly proportional to the resistance
• Directly proportional to the time for which current flows

Mathematically:

H = I²Rt

Where:

• H = Heat produced
• I = Current flowing through the conductor
• R = Resistance of the conductor
• t = Time for which current flows

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Electrical Work

When a potential difference is applied across a conductor, electric charges move through the circuit.

Work is done in moving these charges.

This is called electrical work.

The SI unit of work is:

Joule (J)

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Formula for Electrical Work

Electrical work is given by:

W = VQ

Where:

• W = Electrical work
• V = Voltage
• Q = Electric charge

Since:

I = Q / t

therefore:

Q = It

Substituting:

W = V × It

Hence:

W = VIt

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One Joule of Electrical Work

If:

V = 1 Volt
Q = 1 Coulomb

then:

W = VQ

Therefore:

1 Joule = 1 Volt × 1 Coulomb

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Electric Power

Electric power is the rate at which electrical work is done or electrical energy is transferred.

Mathematically:

Power = Work Done / Time

Therefore:

P = W / t

Where:

• P = Electric power
• W = Electrical work
• t = Time

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Derivation of Electric Power Formula

We know:

W = VIt

Also:

P = W / t

Substituting the value of W:

P = VIt / t

Cancelling t:

P = VI

Therefore:

Electric Power = Voltage × Current

or:

P = VI

Where:

• P = Power
• V = Voltage
• I = Current

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Electric Power Using Resistance

According to Ohm’s Law:

V = IR

We know:

P = VI

Substituting:

P = (IR)I

Therefore:

P = I²R

Hence, electrical power can also be expressed as:

P = I²R

Where:

• P = Power
• I = Current
• R = Resistance

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Important Electric Power Formulae

Basic Power Formula

P = W / t

Power Using Voltage and Current

P = VI

Power Using Current and Resistance

P = I²R

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Unit of Electrical Power

The SI unit of electrical power is the:

Watt (W)

Since:

Power = Energy / Time

therefore:

1 Watt = 1 Joule / 1 Second

or:

1 W = 1 J/s

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Meaning of One Watt

An electrical device has a power of 1 watt when it consumes or transfers electrical energy at the rate of 1 joule per second.

Therefore:

1 Watt = 1 Joule per Second

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Electrical Energy

Electrical energy is the energy associated with electric charges and their movement through an electrical circuit.

In practical terms, electrical energy is the amount of electrical work performed by a device during a certain period of time.

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Formula for Electrical Energy

Electrical energy can be calculated using:

Energy = Power × Time

Therefore:

E = Pt

Where:

• E = Electrical energy
• P = Electric power
• t = Time

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Electrical Energy Using Voltage and Current

Since:

P = VI

and:

E = Pt

Substituting:

E = VIt

Therefore:

E = VIt

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Unit of Electrical Energy

The SI unit of electrical energy is:

Joule (J)

Since:

E = Pt

electrical energy may also be expressed in:

Watt-second (Ws)

Therefore:

1 Joule = 1 Watt-second

or:

1 J = 1 Ws

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Example of One Joule Energy

Suppose:

V = 1 Volt
I = 1 Ampere
t = 1 Second

Then:

E = VIt

E = 1 × 1 × 1

Therefore:

E = 1 Joule

Hence:

1 J = 1 W × 1 s

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Commercial Unit of Electrical Energy

The joule is a relatively small unit for measuring the electrical energy consumed by homes, offices, factories, and other large electrical systems.

Therefore, larger units are commonly used:

• Watt-hour (Wh)
• Kilowatt-hour (kWh)

The kilowatt-hour (kWh) is commonly used as a commercial unit of electrical energy.

Electricity meters measure electrical energy consumed by users, and electricity suppliers use these readings for billing.

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Watt-Hour

A watt-hour (Wh) is the amount of energy consumed when a device uses one watt of power for one hour.

Since:

1 Hour = 60 × 60 Seconds

1 Hour = 3600 Seconds

Therefore:

1 Wh = 1 W × 3600 s

So:

1 Wh = 3600 Ws

Since:

1 Ws = 1 J

therefore:

1 Wh = 3600 J

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Kilowatt-Hour

We know:

1 kWh = 1000 Wh

and:

1 Wh = 3600 J

Therefore:

1 kWh = 1000 × 3600 J

1 kWh = 3,600,000 J

or:

1 kWh = 3.6 × 10⁶ J

Therefore:

1 kWh = 3.6 MJ

where:

MJ = Megajoule

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Important Energy Conversions

1 J = 1 Ws

1 Wh = 3600 J

1 kWh = 1000 Wh

1 kWh = 3.6 × 10⁶ J

1 kWh = 3.6 MJ

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Difference Between Electric Power and Electrical Energy

Electric Power	Electrical Energy
Rate at which electrical energy is transferred or consumed.	Total electrical work or energy consumed over time.
Symbol: P	Symbol: E
Formula: P = W/t	Formula: E = Pt
Also: P = VI	Also: E = VIt
SI unit is watt.	SI unit is joule.
Describes how quickly energy is used.	Describes how much energy is used.

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Quick Revision

Electric Power

Electric power is the rate of doing electrical work.

P = W/t

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Power Using Voltage and Current

P = VI

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Power Using Resistance

P = I²R

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SI Unit of Power

Watt (W)

1 W = 1 J/s

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Electrical Work

W = VQ

Since:

Q = It

therefore:

W = VIt

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Electrical Energy

E = Pt

or:

E = VIt

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SI Unit of Electrical Energy

Joule (J)

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Commercial Unit of Electrical Energy

Kilowatt-hour (kWh)

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Important Conversion

1 kWh = 3.6 × 10⁶ J

or:

1 kWh = 3.6 MJ

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Important Formulae

Joule’s Heating Law

H = I²Rt

Electrical Work

W = VQ

Charge

Q = It

Electrical Work Using Current

W = VIt

Electric Power

P = W/t

Power Using Voltage and Current

P = VI

Power Using Resistance

P = I²R

Electrical Energy

E = Pt

Electrical Energy Using Voltage and Current

E = VIt

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Important Exam Points

• James Prescott Joule studied the heating effect of electric current.
• Joule’s Law of Heating is H = I²Rt.
• Electrical work is the work done in moving electric charge through a potential difference.
• Electrical work is given by W = VQ.
• Since Q = It, electrical work can also be written as W = VIt.
• Electric power is the rate of doing electrical work.
• P = W/t.
• Electric power can be calculated using P = VI.
• Using Ohm’s Law, power can also be written as P = I²R.
• The SI unit of power is watt.
• 1 W = 1 J/s.
• Electrical energy is given by E = Pt.
• Electrical energy can also be written as E = VIt.
• The SI unit of electrical energy is joule.
• 1 J = 1 Ws.
• Watt-hour and kilowatt-hour are larger units of electrical energy.
• 1 Wh = 3600 J.
• 1 kWh = 1000 Wh.
• 1 kWh = 3.6 × 10⁶ J.
• 1 kWh = 3.6 MJ.
• Electricity meters measure electrical energy consumption for billing purposes.