(240)2  
푅 =  
300푊  
1000  
3000  
=
푅 = 19.2Ω  
Total power rating for 4 bulbs = 0.3푘ꢀ  
(b) Calculate the total number of electric  
Step 2: To find the total time  
Total time = 120 hours  
units it consumes in 1 12 hours.  
Solution  
Step 3: To find the total cost  
Given that  
Cost per unt = sh. 100  
Power  
( kW)  
Time  
퐎퐧퐢퐭퐏 퐮퐬퐞퐝  
(khw)  
= [  
] × [  
]
(hours)  
Power  
(in kW)  
Time  
(in hours)  
Total cost = [  
] × [  
]
3000  
1000  
[
]
= [  
] × 1.5hr  
cost per  
× ⌈  
⌉
unit  
= 4.5KWh  
Number of units  
(Energy consumed )  
[
]
[
]
Total cost = 0.3kW × 120 hrs  
= 4.5units  
⌈
⌉
× Tsh. 100  
Total cost = Tsh. 3600  
(c) Find the cost per unit if sh. 900 is paid  
after using it for 3 hours everyday for ten  
days.  
Example 02  
An electric immersion heater is rated at  
3000W, 240V.  
Solution  
퐏퐨퐰퐞퐫  
(in kW)  
퐓퐢퐦퐞  
(in hours)  
Total cost = [  
] × [  
]
(a) Calculate the current and resistance of  
heating element.  
퐜퐨퐬퐭 퐩퐞퐫  
× ⌈  
⌉
퐎퐧퐢퐭  
Solution  
3000  
[
]
⌈ ⌉  
900 = [  
kw] 3 × 10 × y  
1000  
Case I: To find the current  
900 = 90푦  
From  
P = IV  
푦 = 푠ℎ. 100  
The cost per unit is 100sh.  
3000 = 퐟 Ă— 240  
3000  
퐟 =  
Example 03  
240  
Mr. Bagira uses 3 kettles of 800W each, a  
flat iron of 1000W, 3 bulbs 0f 60W each and  
4 bulbs of 75W each. If they are used for 3  
hours every day for 30 days and that one  
unit of electricity costs sh. 200, find the total  
cost of running the appliances.  
퐟 = 12.5퐴  
caseII: To find the resistance  
from  
푉2  
푅 =  
푃
Solution  
5ℎ  
Step 1 : to find the total power  
= 40ꢀ ×  
× 30 푑푎푦푠  
푑푎푦푠  
Kettle  
Flat iron 60W  
bulbs  
75W bulbs  
= 6000ꢀℎ  
3×800  
1×1000  
3×60  
4×750W  
=300W  
= 6푘ꢀℎ  
The electrical energy consumed for  
30 days is 6kWh  
=2400W  
=1000W = 180W  
The total power is given by :  
(b) If the price of a unit of electricity is  
Tsh 229.60, what is the total  
electricity cost of watching this TV  
in 30 days?  
[
]
PT = 2400 + 1000 + 180 + 300 W  
PT = 3 880 W = 3.88 kW  
Solution  
Step 2: to find the total time  
tT = 3 × 30 hrs  
To determine the total cost of  
electricity  
From  
퐄퐧퐞퐫퐠퐲  
퐜퐨퐬퐭 퐩퐞퐫  
퐎퐧퐢퐭  
Total cost = [  
] × ⌈  
⌉
tT = 90 hrs  
(in kWh)  
Step 3: to find the total cost  
= 6 Ă— 229.60  
퐏퐨퐰퐞퐫  
(in kW)  
퐓퐢퐦퐞  
(in hours)  
= Tsh. 1377.60  
Hence, the cost of watching this TV  
for 30 days is Tsh. 1377.60  
Total cost = [  
] × [  
]
퐜퐨퐬퐭 퐩퐞퐫  
× ⌈  
⌉
퐎퐧퐢퐭  
[
]
[
]
⌈
⌉
Total cost = 3.88 × 90 × Sh. 200  
Example 06  
Total cost = í‘ â„Ž. 69 840  
A house has five rooms, each with 60W,  
240V bulb. If the bulbs are switched on  
from 7:00 p.m to 10:30 p.m, determine the  
power (in kilowatt – hour consumed by bulb  
per day. What is the cost of using the power  
in 20days if it costs 150Tsh per 1kWh?  
Example 04  
(a) What is kilowatt hour (kWh)  
Solution  
Kilowatt hour is the electrical energy  
consumed in one hour at the rate of 10000  
watts (1 kilowatt)  
Solution  
Given data  
Power rating = 60W, 240V  
Time = (10:30 – 7:00)  
= 3.5 hours  
Step I  
Total power consumed by 5 bulbs each of  
Example 05  
A television set (TV) rated 40W is switched  
ON for 5 hours every day.  
60W  
푃표푤푒푟 = 60ꢀ × 5  
(a) How much electrical energy in kWh  
does this TV consume in 30days?  
Solution  
3000  
푃표푤푒푟 =  
푘ꢀ  
1000  
푃표푤푒푟 = 60.3푘ꢀ  
퐸푒푛푒푟푔푦 = 푝표푤푒푟 Ă— 푡푖푚푒  
2
(
)
H = (3A) × 20Ω × 120 s  
Step II  
H = 21 600J  
To find the energy (unit consumed) kWh  
Step 2: To find heat gained by water and  
calorimeter  
퐍퐮퐦퐛퐞퐫 퐨퐟 퐎퐧퐢퐭퐏 퐮퐬퐞퐝  
(Energy consumed )  
[
]
퐝 = í‘šę˘íśę˘âˆ†íœƒ + 퐶푐∆θ  
Power  
(in kW)  
Time  
(in hours)  
= [  
] × [  
]
퐝 = 0.1 × 4200∆휃 + 40∆휃  
퐝 = 460∆휃  
[
]
[
]
= 0.3kW × 3.5h  
= 1.05kWh  
Power consumed by five bulbs in each day  
(in kWh ) = 1.05kWh  
Step 3: To find the change in temperature,  
∆휃  
퐻푒푎푡 푠푢푝푝푙푖푒푑  
⌈
⌉
푏푦 푒푙푒ꢂ푡푟푖ꢂ ꢂ푢푟푟푒푛푡  
Step III  
퐻푒푎푡 푔푎푖푛푒푑 푏푦 푤푎푡푒푟  
= |  
|
To find the total energy in 20 days (unit  
consumed) kWh  
푎푛푑 ꢂ푎푙표푟푖푚푒푡푒푟  
[
]
[
]
퐸 = 1.05kWh × 20  
21 600 = 460∆휃  
21600  
∆휃 =  
= 21kWh  
460  
∆휃 = 46.96℃  
Step IV  
To find the total cost in 20 days  
∆휃 ≈ 47℃  
퐄퐧퐞퐫퐠퐲  
퐜퐨퐬퐭 퐩퐞퐫  
퐎퐧퐢퐭  
The temperature rise ≈ 47℃  
Total cost = [  
] × ⌈  
⌉
(in kWh)  
Example 08  
= 21 × 150Tsh.  
(a) If an electric cattle contains 960W  
heating element (unit), what current  
does it take from a 240V mains?  
= Tsh. 3,150  
Hence, the cost of watching this TV  
for 30 days is Tsh. 3,150  
P = IV  
푃
I =  
퐟
Example 07  
A current of 3A flow for 20min through a  
wire of resistance 20Ω. If the wire is totally  
immersed inside a 0.1kg of water in a can of  
960  
I =  
240  
heat  
capacity  
40J/K.  
Calculate,  
the  
I = 4퐴  
temperature rise of water. The specific heat  
capacity of water = 4200J/kgK for water.  
(b) (i) How long will the kettle take to rise  
2kg of water at 15℃ to the boiling  
point, if 90% of the heat produced is  
used raising the temperature of water ?  
Solution  
Step 1: To find heat supplied by electric  
current  
Solution  
퐇 = 퐈ퟐ퐑퐭  
Step 1: Heat supplied by electric current  
ℎ푒푎푡 푠푢푝푝푙푖푒푑 푏푦  
푒푙푒ꢂ푡푟푖ꢂ ꢂ푢푟푟푒푛푡  
⌈
⌉ = 푝표푤푒푟 Ă— 푡푖푚푒  
Example 09  
= 960푡  
Why nichrome is used as a heating element?  
But this heat was only 90%  
Solution  
90  
퐝 =  
× 960푡  
Nichrome is used as a heating element due  
to the following reasons  
100  
퐝 = 864푡 …… (i)  
(i) It is cheap  
(ii) It has high resistance  
(iii)It has high melting point  
(iv)Does not oxidise easily  
Step 1: Heatngained by water to boiling  
point(100℃  
퐝 = í‘šę˘íśę˘âˆ†íœƒ  
= 0.1 × 4200 × (100 − 15)  
DOMESTIC  
ELECTRIC  
= 714, 000퐽 …….. (ii)  
INSTALLATION  
Heat supplied  
⌈
⌉
by electric current  
Domestic wiring: Is the in way which the  
Heat gained by water  
electricity is distributed in the house  
= |  
|
and calorimeter  
Domestic electricity is supplied by two  
cables (wires) such are Live cable (L) and  
Neutral cable (N). A third cable known as  
Earth cable (E)z is also used for extra safety  
714000 = 864푡  
714000  
푡 =  
864  
푡 = 826 푠  
Live cable (L): is the wire that has higher  
p.d relative to the other wires in a cable.  
Normally the main voltage is 240V and so  
the wire is at 240V.  
It will take 826 s for a kettle to rise the  
temperature of water to its boiling point  
(ii) How much would this cost if the  
charge is 300Tsh. For 1kWh?  
Live wire (Red/brown) is connected to the  
live pin/ fuse  
Solution  
Neutral cable (N):-is the wire that has zero  
p.d that originates from power substation.  
The neutral wire (blue/black) is connected to  
the neutral pin.  
Power = 960W = 0.96kW  
Time = 826 s = 0.2294 h  
퐏퐨퐰퐞퐫  
퐓퐢퐦퐞  
(in hours)  
Total cost = [  
] × [  
]
(in kW)  
× ⌈  
퐜퐨퐬퐭 퐩퐞퐫  
⌉
퐎퐧퐢퐭  
Example  
[
]
[
]
= 0.96kW × 0.2294h  
⌈
⌉
× Tsh. 300/kWh  
This The neutral cable is earthed (connected  
to the ground at the power station). Why?  
= Tsh. 66  
The total cost will be Tsh. 66