# Commercial Unit : Kilowatt-Hour class 10 | cbse24.com

Note: Before going to understand the Commercial Unit first understand electrical energy.

## Electrical Energy:

Electrical Power =Work is done by electrical current / Time taken

According to the law of conservation of energy, Work is done by electrical current=Electrical energy consumed

so E=P x t

Unit of energy = Watt x hour or joule

• 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.
• One Watt-Hour is the amount of electrical energy consumed when an electrical appliance of 1 Watt power is used for 1 hour.
• We will use the commercial unit of electrical energy in kilowatt-hour.

### Commercial Unit Of Electrical Energy(Kilowatt-Hour):

The SI unit of electrical energy is the joule. Joule represents a very small quantity of energy, so for commercial purposes, we use a bigger unit of electrical energy which is called "kilowatt-hour".

1 kilowatt-hour (1 Unit)=1 kilowatt-hour is the amount of electrical energy consumed when an electrical appliance having a power rating of 1kilowatt is used for 1 hour.

Example = Suppose 10 bulbs each one of rating is 100 watts run 1 hour then they consumed 1kwh mean 1Unit of electricity.

### The relation between kilowatt-hour (Unit) and joule:

1 Unit=1kilowatt-hour=1kilowatt for 1 hour=1000 watt for 1hour

$1unit=1kilowatt-hour=1000watt\times 3600second=3600000watt.second$

$3600000watt.second=3.6\times 10^{6}joule$

$1Unit=1kilowatt-hour=3.6\times 10^{6}joule$

Note:  1kilowatt-hour=3600000 joules ($3.6\times 10^{6}j$)

### How commercial Unit is measured and by which device:

• Kilowatt-hour is the "Unit" of electrical energy for which we pay to the electricity supply department of your state. One "Unit" of electricity costs anything maybe 4 to 10 rupees(lower in rural and higher in an urban area).
• By electricity meter, we found how many units we consumed in a day according to what load we use.
• If we multiply the Unit consumed on that day with the Unit cost then we can find out daily money consumed by you. Example: If that particular day your consumed Unit is 10 and the cost of per Unit in your area be 8 rupees then your cost that day will be=10 unit x8 rupee=80 rupee.

 Electricity meter

### A mixed question of S.Chand and NCERT of this topic:

Q1:-How much energy is consumed when a current of 5 amperes flows through the filament of a heater having a resistance of 100ohms for two hours? Express it in joules?

Ans- $W=p*t=i^{2}Rt=5^{2}*100*7200=18\times+10^{6}j$ (convert hour in the second 2h=7200s)

Q2.An electric bulb is connected to a 220 v power supply line. If the bulb draws a current of 0.5A, calculate the power of the bulb.

Ans- P=Vx I = 220 x0.5 =110 w

Q3.In which of the following cases more electrical energy is consumed per hour?

(I) A current of 1 ampere passed through a resistance of 300 hours?

(ii)A current of 2 A passed through a resistance of 100 ohms?

Ans- (a) $W=i^{2}\times+R\times+t=1^{2}\times+300\times+3600=1.08\times+10^{6}$

(b) $W=i^{2}\times+R\times+t=2^{2}\times+100\times+3600=1.44\times+10^{6}$

so in case 2, you can see more energy is consumed

Q3.An electric kettle rated at 220 v, 2.2kw, works for 3 hours. Find the energy consumed and the current drawn.

Ans- E=P x t = 2.2kw x 3h =6.6 kwh

we know P=V x I =2.2 x 1000 w = 220 x I
so I=2200/220=10A

Q4.In the house, two 60w bulbs are lighted for 4 hours, and three 100w bulbs for 5 hours every day. Calculate the electric energy consumed in 30 days.

Ans-E1=n x P x t x days =2 x 60 x 4 x 30=14400wh=14.4kwh

E2=n x P x t x days =3 x 100 x5 x 30=45000wh=45kwh

Etotal=E1+E2=14.4+45=59.4kwh

Note- n= number of bulb

Q5 a bulb is rated as 250v,0.4A. Find its (I) Power (ii) Resistance.

Ans- (1) P=V x I= 250 x 0.4 =100 w

(2) $P=Vi=100=0.4^{2}R$

R=100/0.16 =625 ohm

Q6
For a heater rated at 4kw and 220 v, calculate.

(i)
the current

(ii) the resistance of the heater

(iii) the energy consumed in 2 hours and

(iv) the cost if 1kwh is priced at 4.60 rupees.

Ans- (1) Given p=4kw(or 4000w )P= V x I =4kw=4000w=220 xI

so I=4000/220=18.18 A

(2) $P=\frac{V^{2}}{R}=4000w=\frac{220^{2}}{R}$

so R =220 x 220/4000=48400/4000=12.1 ohm

(3) E=P x t = 4kw x2h =8kwh

(4) cost= no of unit x per unit price

(8kwh=8unit)
so cost= 8 x 4.60=36.80 rupees

Q7.An electric motor takes 5 A current from the 220 volt supply line, calculates the power of the motor and electrical energy consumed by it in 2 hours.

Ans.P= V x I=220 x 5 =1100 watt =1.1kw

E= P x t = 1.1kw x 2 h = 2.2kwh

Q8.Which uses more energy a 250w TV set in 1 hour or a1200w toaster in 10 minutes?

Ans-(a) (Energy for Tv Etv=P x t= 0.25kw x 1h=0.25kwh

(b) (Energy for toaster) Etostar = P x t =1.2kw x 1h =1.2kwh

so toaster takes more energy then TV

Note=1kw=1000w and 250w=0.25kw and 1200w=1.2kw

Q9.Calculate the power used in the 2ohm resister in each of the following circuits:

(i) A 6v battery in series with 1ohm and 2ohm resistor.

(ii) A 4v battery in parallel with 12 ohms and 2-ohm resister.

Q10. Two lamps, one rated 40w at 220v and the other 60w at 220 v are connected in parallel to the electric supply at 220 v

(a)Draw a circuit diagram to show the connections

(b) Calculate the total energy consumed by the two lamps together when they operate for one hour.

(c) Calculate the current drawn from the electric supply.

Q.11.An electric kettle connected to the 230 v mains supply draws a current of 10 A. Calculate

(a) the power of the kettle

(b) the energy transferred in 1 minute

Q12. A 2kw heater, a 200w TV and three 100w lamps are all switches on from 6p.m to 10 pm. What is the total cost at Rs. 5.50 per kWh?

Q13. What is maximum power in kilowatt of the appliance that can be connected safely to a 13 A,230 v mains socket?

Q14.An electric fan runs from the 230 v mains. The current flowing through it is 0.4A.at what rates electrical energy transferred by the fan?

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