The power expanded in heating a resistor or turning a motor depends upon the potential difference b/w the terminals of the device and electric current passing through it.
Power p = V x I watts
Now if an electrical appliance is operated at a potential difference of 1 volt and the device carries a current of 1 ampere, then power becomes 1 watt. That is
1 watt = 1 volt X 1 ampere
1 w = 1 V A means
One watt is the power consumed by an appliance which when operated at a potential difference of 1 volt carries a current of 1 ampere.
Some other formulae of calculating the electric power:
We have just obtained a formula for calculating electric power ; which is
P = V X I
We have other formulae of electric power which are following;
We have , P = v x I-----------------------(I)
Now from ohm’s law we have V/I = R
Or v = I X R , now from 1
P = I2 R where , I = current and R = resistance
P = V x I -------------------- (i)
Also from ohm’s law we have V/I = R or I = V/R
Putting this value of I in equation (i)’ we get
P = V2/R , where V = potential difference and R = resistance of wire
Note: power is inversely proportional to the resistance of wire.
Power- voltage rating of electrical appliance:
We know that every electrical appliance like an electric an electric bulb , radio or fan has a label or engraved plate on it which tells us voltage and electric power consumed by it. For example, if we look at a particular bulb in our home, it may have the figures 100 w – 220 V written on it. Now 100w means this bulb has a power consumption of 100 w and 220 V means that it is to used on a voltage of 220 volts. The power rating of an electrical appliance tells us the rate at which electrical energy is consumed by the appliance.
For example: the power rating of 100 w on the bulb means that it will consume electrical energy at the rate of 100 joules per second.
An electrical formula for calculating electrical energy:
We have already studied that;
Electric power = work done by electric current / time taken
Now according to the law of conservation of energy,
Work done by electric current = electric energy consumed
Power = electric energy/ time
Electric energy = power x time or E = P x t
The electrical energy consumed by an electrical appliance is given by the product of its power rating and the time for which it is used.
From this we conclude that the electrical energy consumed by an electrical appliance depends on two things
In the formula: electrical energy = power x time, if we take the power in ‘watts’ and time in ‘ hours’ then the electrical energy becomes ‘watt – hours’. (Wh)
One watt – hour is the amount of electrical energy consumed when an electrical appliance of 1 watt is used for one hour. Now we have describe the commercial unit of electrical energy of electrical energy called kilowatt – hour.
One kilowatt – hour is the amount of electrical energy consumed when an electrical energy consumed when an electrical appliance having power rating of 1 kilowatt is used for 1 hour.
Relation b/w kilowatt – hour and joule: One kilowatt – hour is the amount of electrical energy consumed when an electrical energy consumed when an electrical appliance having power rating of
1 kilowatt is used for 1 hour.
That is; 1 kilo watt – hour = 1 kilo watt for one hour
= 1000 watts for 1 hour
But : 1 watt = 1 joule / 1 second
1 kilo watt – hour = 1000 joules / second for one hours and one hour = 3600 seconds
Or 1 kilo watt hour = 36,00, 000 joules = 3.6 x 10 6 joules
Note : kilowatt – hour is the “unit” of electrical energy for which we pay the electricity.
Heating effect of current: When an electric current is passed through a high resistance wire like nichrome wire, the resistance wire becomes hot and produced heat. This is known as heating effect of current. The role of resistances in the circuits is same as the friction in the machines.
Since a conductor, say a resistance wire, offers resistance to the flow of the current, so work must be done by a current continuously to keep itself flowing. We will calculate the work done by a current I when it is passing through a resistance R for time t. Now when an electric charge Q moves against a potential difference V, the amount of work done is given by
W = Q X V
From the definition of the current we have, I = Q /t or Q = I t
And from ohm’s law, we have V/ I = R or potential difference , V = I x R
Now putting Q = I x t and V = I x R
We have W = I2 X R x t or
Heat produced, H = I2 X R x t joules
It is clear that the heat produced in a wire is directly proportional to
Applications of the heating effect of current:
The important applications of the heating effect of electric current are following
