In this article, I will explain the concept of **electrical energy**. Electrical energy is one of the fundamental electrical quantities widely used in electrical and electronic circuits. It is the measure of the total amount of electric power consumed over a certain period of time. In any electric circuit, electrons move in a particular direction to do some work. Hence, to move these electrons, some external agent is required to do work. This work done is expended in the circuit in the form of electrical energy.

## What is Electrical Energy?

**Electrical energy** is defined as the capability of charged particles to do work in an electric circuit.

Electrical energy can be of two types namely, potential energy and kinetic energy.

If the charge carriers or electrons have the energy due to their position at a point of high potential, then the electrical energy is termed as potential electrical energy.

On the other hand, if the electrons have energy due to their movement through a conductor, then it is called kinetic electrical energy.

Technically, electrical energy is defined as the total amount of work done in an electric circuit over a certain period of time.

## Electrical Energy Formula

As we know, electrical energy is the total amount of work done in an electric circuit in a certain period of time.

Thus, if W joules is the amount of work done in an electric circuit in a time t seconds. Then, the electrical energy expended in the circuit is,

Electrical Energy = Rate of Work Done × Time

As we know, the rate of work done in an electric circuit is called electric power. Therefore, we get,

Electrical Energy = Electric Power × Time

∴ Electrical Energy = p × t

Where, p is the electric power in watts.

Also, in an electric circuit, the electric power is given as the product of voltage and current i.e.,

$$p=v.i$$

Therefore, the electrical energy will be,

$$w=p×t=vi×t$$

Where, w is the electrical energy.

Thus, electrical energy is the product of voltage, current, and time.

## Relation between Electrical Energy and Resistance

According to Ohm’s law,

$$v=iR$$

And

$$i=\frac{v}{R}$$

Substituting the values of voltage or current in the expression of electrical energy, we get,

$$w=i^2 Rt=\frac{v^2}{R} t$$

This expression shows the relation between electrical energy and resistance.

## SI Unit of Electrical Energy

The SI unit of electrical energy is Joule, denoted by J.

But, in electrical and electronic engineering, the unit of electrical energy is expressed in terms of units of electric power and time, as follows:

Unit of electrical energy = Watt × second

Where, watt is the unit of power and second is the unit of time.

Hence, the practical unit of electrical energy is Watt-second (Ws).

Some other units of electrical energy used are given below:

- When power is expressed in watts and time in hours, then the unit of electrical energy is Watt-hour (Wh).
- When power is expressed in kW and time in hours, then the unit of electrical energy is kilowatt-hour (kWh).

## Commercial Unit of Electrical Energy

In practice, the utility companies measure electrical energy in kWh. Hence, kWh is called the commercial unit of electrical energy.

kWh is also known as Board of Trade Unit (B.O.T.) or simply unit.

1 Unit or BOT Unit = 1 kWh = 1000 Wh

Hence, when we say that our electricity meter is showing 200 units of electricity, it means that we have consumed 200 kWh of electrical energy.

We can define the BOT unit or kWh as follows:

1 kWh is the amount of electrical energy expended in an electric circuit if an electrical load of 1 kW or 1000 Watts is supplied for 1 hour.

## Use of Electrical Energy Formula

**Case I** – Electrical energy is given by,

$$W=VIt$$

This formula of electrical energy can be applied to any kind of load.

**Case II** – Electrical energy is also given by,

$$W=I^2 Rt=\frac{V^2 }{R}t$$

This formula of electrical energy can only be used to calculate the electrical energy consumed by a device that converts entire electrical energy into heat like an electric heater, electric bulb, electric kettle, etc.

## Numerical Examples Based on Electrical Energy

**Example (1)** – An electric motor has a rated voltage of 220 volts and a rated current of 16 A. If this motor is operated for 2 hours, then how much electrical energy will it consume in kWh?

**Solution** – Given data,

Rated voltage (*V*) = 220 V

Rated current (*I*) = 16 A

Time (*t*) = 2 hours

The electrical energy consumed by the motor is,

*W = VIt* = 220 × 16 × 2 = 7040 Wh

In kWh, the electrical energy consumed by the motor is,

⸫ *W* = 7.04 kWh

**Example (2)** – An electric heater of 1.5 kW working for 3 hours per day. If each unit of electrical energy costs 6 INR. What will be the electricity bill for the month of January?

**Solution** – Given data,

Power (P) = 1.5 kW

Time (t) = 3 hours

Number of days (January) = 31

Cost per unit (in INR) = 6

The electrical energy consumed by the heater per day is,

*W _{day} = P × t* = 1.5 × 3 = 4.5 kWh

Thus, the total electrical energy consumed in 31 days is,

W = 4.5 × 31 =139.5 kWh = 139.5 Units

Hence, the electricity bill for the month of January is,

Bill Amount = W × Rate per unit = 139.5 × 6

⸫ Bill Amount = 837 INR

**Example (3)** – An electric heater has a resistance of 500 Ω. Calculate the electrical energy consumed by the heater if a voltage of 120 V is applied for 2 hours.

**Solution** – Given data,

Resistance (*R*) = 500 Ω

Voltage (*V*) = 120 V

Time (*t*) = 2 hours

The electrical energy consumed by the heater is,

$$W=\frac{V^2}{R}t=\frac{500^2×2}{500}$$

⸫ W = 1000 Wh = 1 kWh

**Example (4)** – An electric current of 5 A is flowing through a copper wire of 0.5 Ω resistance. Calculate the amount of energy consumed in the wire in 5 hours.

**Solution** – Given data,

Electric current (*I*) = 5 A

Resistance (*R*) = 0.5 Ω

Time (*t*) = 5 hours

The electrical energy consumed in the wire is,

$$W=I^2 Rt=5^2×0.5×5$$

⸫ W = 62.5 Wh

## Conclusion

In conclusion, electrical energy is the measure of the total amount of work done in an electric circuit in a certain period of time. In an electric circuit, we can calculate the electrical energy expended as the product of electric power and time. Commercially, the electrical energy is measured in kWh or Unit.

In this article, I have explained the concept of electrical energy, its SI unit, formula, and numerical examples. If you have any queries related to this topic, please let me know in the comment section.