Definition of Electrical Power

Electrical power is the rate at which electrical energy is converted into another form of energy (such as heat, light, or mechanical energy). It tells us how fast electrical work is done. Mathematically,

where:

• $P$ = electrical power (in watts, W)
• $W$ = electrical work or energy (in joules, J)
• $t$ = time (in seconds, s)

Expression in Terms of Voltage and Current

SI Unit of Power

The SI unit of electrical power is the watt (W). 1 watt=1 joule per second. That means if an electrical device converts 1 joule of energy per second, its power is 1 watt.

Larger Units of electrical power

Because many electrical devices consume large amounts of power, we use bigger units:

Electrical Energy

The energy produced due to the flow of electrons is known as electrical energy. It’s SI unit is Joule. If ‘I’ current is flowing through a circuit for a time of ‘t’ seconds, then from the definition of potential difference.

1 J electrical work:
We have,
    W = Q X V
   = 1C X 1V
    = 1 J

It is defined as the amount of work done when 1 coulomb of charge is moved under a potential difference of 1 volt.

 or,  Q =I t …………..(2)

Substituting the value of ‘Q’ in (i), we get
W = I X t X V

Thus we can say, electrical energy depends on current, voltage and time of flow of current.

Similarly, from Ohm’s law,

We have,
V= I X R
W = I X t (I X R)
      = I² R t

Thus, the electrical energy will be converted into heat energy and the electrical energy is said to be consumed by the electric circuit. This is known as heating effect of current and the heat developed in a circuit is given by the relation,

= I² R t

This relation is known as Joules law of heating. According to it, the heat produced on the conductor is directly proportional to:
i. Square of magnitude of current flowing through the conductor.
ii. Resistance of conductor
iii. Time for which the current is passed over to the conductor.

Electric Power:

The amount of electrical work done per unit time is called the electric power. Its SI unit is watt.

Similarly, the electric power can also be expressed as,

Electrical Energy Consumption:

We have

Or, Electric energy consumed = Electrical power X time taken
Now, if P = 1 watt, t = 1 sec
Electric energy = 1 watt X 1 sec
= 1 watt-sec

Hence watt-sec is very smaller unit of electrical energy. So in home and for commercial purposes, we use higher units of it. i.e watt-hour, kilowatt-hour(kwh). watt-hour

1 watt-hour = 1 X 60 X 60 watt-sec
= 3600 watt-sec
= 3600J

Kilowatt – hour
1 kilowatt-hour = 1000 X 60 X 60 watt-sec
= 3600000 J

This 1 kilowatt-hour simply can be said as 1 unit electrical energy consumption.

Kilowatt- hour (kwh):

When an electrical appliances of 1000 watt (1 kw) is used for 1 hour, then the electrical energy consumed is said to be 1 kilowatt-hour (kwh). Simply it is called 1 unit electrical energy consumption.

1 watt electrical power
We have,
P = I X V
= 1A X 1V
= 1 watt

If 1 A current is flowing through a conductor under a potential difference of 1 volt, then the power consumed is said to be 1 watt electrical power.

Similarly,

or,  P=1

Thus, if 1 joule of work is done in moving the charge from one point to another within the circuit in 1 second, then the power consumed is said to be 1 watt power.

Note:
If a bulb is rated with 100 watt, it means the bulb can convert 100 J of electrical energy into heat and light energy in 1 second.

Numerical
1. The resistance of the element of heater is 900Ω and current of 1.5A is flowing through the circuit. Find the power dissipated in the circuit.

Given That

2. An electric heater operates on 220 V and draws a current of 6 A. Calculate the power consumption.

3. The current passing through a filament lamp is 2A. If it is connected to a 12 V power supply. Calculate the resistance of filament and power consumed by the lamp.

5. An electric heater of 220V is used on 8A. Find the power consumed by it. Also find the cost of using the heater for one hour if the rate of electricity is Rs. 6 per unit.

6. In a house, 5 bulbs of 60 watt glows for 4 hours a day, an electric press of 750 watt for an hour everyday and 3 electric fans of 150 watt is used for 8 hours a day. Find the total electrical energy consumed in 15 days. Also calculate the cost of electricity at Rs. 12 per unit.

7. In a house, 8 bulbs of 100 watts glows for 5 hrs a day, an electric iron of 800 watt for an hour everyday and 2 electric heaters of 1000 watt for 6 hours a day. Find the cost of electricity for a month of 30 days if the rate of electricity is Rs. per unit.

Compiled By Er. Basant Kumar Yadav