# Class 10 electricity Notes : Electric Power

## 12. Electric Power

• Rate of doing work or the rate of consumption of energy is known as POWER
Mathematically,

• SI unit of power is Watt which is denoted by letter W. The power of 1 Watt is a rate of working of 1 Joule per second. Actually Watt is a small unit, therefore , a bigger unit of electric power called Kilowatt is used for commercial purposes. Also ,
1 kilowatt = 1000 Watts
So,
" the rate at which electric work is done or the rate at which electric energy is consumed is called electric power "
• We will now derive formula for the calculation of electric power.
From equation 14 we know that

Now we know that work done W by current I when it flows for time t under a potential difference V is given by

Putting this value of work done in equation 16 we get

Hence,
Electric Power = voltage x current

### 12 (a) Power in terms of I and R

• From equation 17 we know that
$P=VI$
Now from Ohm's law

Putting above equation in equation 15 we get
$P=I \times R \times I$
Power , $P=I^2 \times R$
• Above formula is used to calculate power when only current and resistance are known to us.

### 12 (b) Power in terms of V and R

• From equation 17 we know that P=VI Now from Ohm's law

Or we have

• Putting this value of I in equation 15 we get
$P = V \times \frac{V}{R}$
$P = \frac{V^2}{R}$
This formula is used for calculating power when voltage V and resistance R is known to us.
• It is clear from the above equation that power is inversely proportional to the the resistance.
• Thus the resistance of high power devices is smaller then the low power ones. For example , the resistance of a 100 Watt bulb (220 V) is smaller then that of 60 Watt (220 V) bulb.
• We have three formulas for calculating electric power. These are
(1) $P = V \times I$
(2) $P= I^2 \times R$
(3)$P = \frac{V^2}{R}$
You must memorize these formulas as they would be used to solve numerical problems.
• When electrical appliance consumes electrical energy at the rate of 1 Joule per second , its power is said to be 1 Watt.
• Rate at which electric work is done or the rate at which electric energy is consumed , is called electrical power.