Unit of electrical energy and work

Author: Matthew David

Unit of electrical energy and work

Introduction to unit of work:

Work is a physical unit which is also called as mechanical work. Work is defined as the energy that is transferred by the force that is acting on the object through a distance. Work is a scalar quantity like energy. The work is calculated in terms of joules. Joules is the SI unit of work.

Consumers of electricity do not pay for the amount of current or unit of electrical voltage their appliances take. The cost is based on the amount of energy electrical energy consumed. However, electrical energy for this purpose is not measured in joule as it is a very small unit. Electrical energy is usually measured in a unit called a kilowatt-hour (kWh) which is the amount of electrical energy consumed when an electrical appliance with a power rating of 1 kilowatt is used for 1 hour.

1 kWh = 1 kW x 1 hour = 1000 Wx 3600 s = 3,600,000 J

The kilowatt-hour (kWh) is called the board of trade unit or simply the unit.

Calculation of energy consumption at home

The electric meter installed in every house measures the electricity

 consumption in kWh. Our electricity consumption bill is made on

the basis of the number of units consumed by us during a given

period. A sample calculation is as follows.

• A 100 W bulb consumes energy at the rate of 0.1 kWh per hour. Therefore if the bulb is used for 5 hours a day, it uses up 0.1x5 x 30 = 15 kWh energy every month.

• If 4 such bulbs are used, total consumption = 60 kWh or 60 units.

• A fan with a rating of 60 W consumes 0.06 kWh energy every hour. Therefore if 4 fans are used for 10 hours a day, the energy used up in a month is 0.06 x4xl0x30 = 72 kWh or 72 units.

• If a 250 W refrigerator works for 12 hours a day, energy consumption = 0.25x12x30 = 90 kWh or 90 units in a month.

• If a 2 kW AC works for 6 hours a day, energy consumption = 2 x 6 x 30 = 360 kWh or 360 units.

Total energy consumed every month = 60 + 72 + 90 + 360 = 562

units

If cost of electricity is Rs 4 per unit, then monthly electricity bill

will be Rs 4 x 562 = Rs 2248 .

Representation of work

According to the theorem of work and energy, When an external force act on any object it causes the kinetic energy to change from E_k1 to E_k2, then the work W is represented as

`W= Delta E_k= E_k_2 - E_k_1 = 1/2(m v_2^2- m v_1^2)`

If the resultant force F that is acting on an object when the object is displayed at a certain distance d, and force and displacement will act in parallel direction to each other, The work done on an object is represented as the product of force F multiplied by the distance d

`W=F.d`

When the force and displacement are in same direction and parallel, then the mechanical work will be positive. If the force and displacement are in opposite direction and are parallel that is anti parallel to each other then the mechanical work will be negative.

When the force and displacement are perpendicular to each other then the work done by the force will be equal to 0. There will be no work done if they are perpendicular.

The Force and the displacement are vector quantities and by using the dot product these are combined to calculate the mechanical work which will be a scalar quantity:

`W=F.d=F.d cos theta`

Where F represents the force and d represents the displacement vector and theta represents the angle between the force and displacement.

Unit of work:

Since the work that is done is represented by W=F.S, So the units of work is represented as force times the length. The SI unit of work is represented as Joule(J) or Newton-meter(Nm)

 1 J = 1 Nm

In the cgs system the unit of work is erg or dyne cm.

1 joule is equal to `10^7` ergs.

 The dimensional formula of work is represented as `[ML^2T^-2]`

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