Electric power

Expression for work done:

\[W=VIt\]

\[W=I^2Rt\]

\[W=\frac{V^2t}{R}\]

ELECTRIC POWER 

Electrical power is the rate at which electric energy is dissipated or consumed in an electric circuit. 

The power P is given by
\[P=\frac{W}{t}\;\;\text{ or  } \;\;P=\frac{E}{t}\]
\[P=VI\]
\[P=I^2R\]
\[P=\frac{V^2}{R}\]

SI Unit:

 The SI unit of electric power is watt (W). 

Definition of 1 watt: 

It is the power consumed by a device that carries 1 A of current when operated at a potential difference of 1 V. Thus, 

1 W = 1 volt × 1 ampere = 1 V A 

Bigger unit of power:

(a) kilowatt (kW)

         1 kW = 1000 W

(b) Megawatt (MW)

          1 MW = 1000 kW = 1000000 W = \(10^6\) W

Watt-hour 

Watt-hour (Wh) is the unit of energy. 
One watt-hour is the energy consumed when 1 watt of power is used for 1 hour. 

Kilowatt-hour(kWh)

Kilowatt-hour is the commercial unit of energy 
The commercial unit of electric energy is kilowatt-hour (kWh), commonly known as ‘unit’. 

One kilowatt-hour is the energy consumed when 1 kilowatt of power is used for 1 hour. 

Relation between kilowatt-hour and joule 
Energy = Power x time
1 KWh = 1000 watt x 3600 second
             =  3.6 x \(10^6\) watt second
             =  3.6 x \(10^6\) joule (J)

NOW CHECK YOUR PROGRESS!!! 

1. Which uses more energy, a 250 W TV set in 1 hr, or a 1200 W toaster in 10 minutes? 

2. Two lamps, one rated 100 W at 220 V, and the other 60 W at 220 V, are connected in parallel to electric mains supply. What current is drawn from the line if the supply voltage is 220 V? 

3. Compare the power used in the 2 Ω resistor in each of the following circuits: (i) a 6 V battery in series with 1 Ω and 2 Ω resistors, and (ii) a 4 V battery in parallel with 12 Ω and 2 Ω resistors. 

4. Several electric bulbs designed to be used on a 220 V electric supply line, are rated 10 W. How many lamps can be connected in parallel with each other across the two wires of 220 V line if the maximum allowable current is 5 A? 

5. An electric bulb is rated 220 V and 100 W. What will be the power consumed when it is operated at 110 V? 

6. An electric motor takes 5 A from a 220 V line. Determine the power of the motor and the energy consumed in 2 h. 

7. An electric refrigerator rated 400 W operates 8 hour/day. What is the cost of the energy to operate it for 30 days at Rs 3.00 per kW h? 

8. An electric bulb is connected to a 220 V generator. The current is 0.50 A. What is the power of the bulb?