In the previous section we saw that household circuits should be in parallel mode. In this section, we will see the details of an actual household circuit.
We will write it in steps:
1. Consider fig.12.6 below:
• 4 lines are passing through the electric post. We can obtain electrical energy from them.
2. For household purposes, we need only two lines:
♦ Any one phase line and
♦ The neutral line.
• Here we have chosen the red phase line.
3. Both the lines first enters the kwh metre.
• From this metre, we get 'the amount of energy used by the consumer'. We will see details later in this section.
4. The main line then enters the main fuse box.
• This is for safety purposes.
• When current flows above the accepted level, the fuse wire melts and thus, the circuit is broken.
• We have already seen the working of the safety fuse.
5. Then the lines enter the main switch.
• The current flow into the house can be stopped or resumed at any time by using the main switch.
6. After that, both the lines enter the ELCB. (Earth Leakage Circuit Breaker)
• This device breaks the circuit (and thus stops the flow of current) if it detects any flow of current in the 'earth wire'.
• If even small quantities of current flows through the earth wire, it will be due to faults in the circuit.
• So it is essential to break the circuit immediately
• We will learn about earth wire in the next section
• However, devices which are even more advanced than the ELCB, are available today.
7. After that, both the lines enter the MCB distribution board. We have already learned about MCB.
• It is a safety device which will break the circuit if there is any fault in the circuit. Details here.
• What we have now, is a 'MCB distribution board'. This board combines two functions:
(i) It helps to take out branches from the phase line
♦ Each of those branch will go into it's own circuit
♦ One such circuit will be available for each room in the house
(ii) It provides the 'circuit breaking safety' for each of those circuits
8. So, after branching at the 'MCB distribution board', we will get several 'live lines'. In our present case, we have 3 'live lines'.
• Each live line goes into it's own circuit.
• One such circuit is shown in detail. This circuit has 3 appliances:
a bulb, a fan and a 3 pin socket
9. These 3 appliances should be connected in parallel
• In the fig.12.6, they are indeed connected in parallel.
• If we have more space to draw, that circuit can be drawn as shown in fig.12.7 below:
• Now the 'parallel mode' is more clear
• The reader may compare the switch board in fig.12.7 with that in fig.12.6 and verify that, they are the same.
• In fig.12.7, notice how 'an additional bulb taken from the 3 pin socket' will effectively complete the flow of current through the socket. The green line is the 'earth line'. We will see it's details in the next section.
■ The system shown in fig.12.6 is called the tree system.
Now we will see the kwh meter. We will write it in steps:
1. We have learned about 'electric power' (Details here)
• Consider an appliance on which it is marked as '1000 watts'
• That means, that appliance will consume an energy of 1000 joules in one second
2. If the consumer uses that appliance for one hour, how much energy will be used?
Ans: 1000 × 60 × 60 = 3600000 joules = 3600 kilo joules
• The consumer will have to pay money for this 3600 kilo joules
3. But the distribution companies do not measure energy in joules or kilo joules.
■ They use another unit: kilowatt hour
4. Let us see how this unit is derived:
• We know that 'power' is the ratio of Energy to time. That is:
Power = Energy⁄time
• Multiplying both sides by 'time', we get:
Power × time = Energy⁄time × time
5. But [Energy⁄time × time] = Energy
• Then (4) becomes: Power × time = Energy
• So, to get 'amount of energy used', we can multiply the following two quantities:
(i) Power of the appliance
(ii) Time for which the appliance is used
6. We can write:
Amount of energy used by an appliance
= Power of the appliance × Time for which the appliance is used
7. Based on this, we can derive 'units':
• unit of energy = unit of power × unit of time
⟹ unit of energy = watts × sec
8. For large values, we can use:
• kilowatts instead of watts (∵ 1000 watts make up one kilo watt)
• hour instead of sec (∵ 3600 seconds make up one hour)
■ So we get:
Unit of energy = kilowatt hour (kwh)
• This unit is used by the distribution companies.
9. The companies use the simple term: 'units'
■ 1 unit = 1 kwh
An example:
• If a consumer uses '25 units' of electricity, it means that, he uses 25 kwh of electrical energy
10. On many occasions, we will want to know the 'number of units' consumed in our homes and offices. So let us derive an easy method:
• The two information that we will be having are:
♦ Power of the appliance (in watts)
♦ Time for which the appliance is used (in hours)
• Based on the above two, we must be able to quickly find the 'number of units'. Let us try:
We will write the steps:
(i) When 'power' is multiplied by 'time', we get 'energy'.
• So '(watt × hour) = watt hour' is energy
(ii) But we want 'kilowatt hour'
• So we must divide 'watt hour' by 1000
• Then we will get 'kwh' or the 'number of units' directly.
(iii) We can write the formula:
Let us see an example:
Solved example 12.1
A grinder of power 750 W works for 2 hours. Calculate the energy consumed
Solution:
1. Given that, power = 750 W, Time = 2 hours
2. We have:
Substituting the values, we get:
Energy (kwh) = 750×2⁄1000 = 1.5 kwh = 1.5 units
Another method:
1. Given that, power = 750 W
So the grinder consumes 750 joules every second
2. In 2 hours, there are (2 × 3600) seconds
So energy consumed in 2 hours = 750 × 2 × 3600 = 5400000 joules
3. We have to convert this into kwh:
(i) 1 kilowatt = 1000 watts = 1000 joules per second
• 1 hour = 3600 seconds
(ii) So energy of 1 kwh = (1000 3600) = 3600000 joules
(iii) So 1 joule = 1⁄3600000 kwh
(iv) So 5400000 joules = (5400000 × 1⁄3600000) = (54⁄36) = 1.5 kwh
• The kwh meter is installed by the distribution companies.
• It directly shows the consumption in kwh
• So we need not calculate the consumption in joules
• Some images can be seen here.
Solved example 12.2
In a house, in a day,
• 5 CF lamps each of 20 W, work for 4 hours
• 4 fans each of 60 W, work for 5 hours
• 1 TV of 100 W, works for 4 hours
What will be the consumption shown by the kwh meter per day?
Solution:
1. Power consumption of 1 CF lamp = 20×4⁄1000 = 0.08 kwh
∴ Power consumption of 5 CF lamps = 0.08 × 5 = 0.4 kwh = 0.4 units
2. Power consumption of 1 fan = 60×5⁄1000 = 0.3 kwh
∴ Power consumption of 4 fans = 0.3 × 4 = 1.2 kwh = 1.2 units
3. Power consumption of 1 TV = 100×4⁄1000 = 0.4 kwh = 0.4 units
4. Total consumption = 0.4 + 1.2 + 0.4 = 2 units
We will write it in steps:
1. Consider fig.12.6 below:
 |
| Fig.12.6 |
2. For household purposes, we need only two lines:
♦ Any one phase line and
♦ The neutral line.
• Here we have chosen the red phase line.
3. Both the lines first enters the kwh metre.
• From this metre, we get 'the amount of energy used by the consumer'. We will see details later in this section.
4. The main line then enters the main fuse box.
• This is for safety purposes.
• When current flows above the accepted level, the fuse wire melts and thus, the circuit is broken.
• We have already seen the working of the safety fuse.
5. Then the lines enter the main switch.
• The current flow into the house can be stopped or resumed at any time by using the main switch.
6. After that, both the lines enter the ELCB. (Earth Leakage Circuit Breaker)
• This device breaks the circuit (and thus stops the flow of current) if it detects any flow of current in the 'earth wire'.
• If even small quantities of current flows through the earth wire, it will be due to faults in the circuit.
• So it is essential to break the circuit immediately
• We will learn about earth wire in the next section
• However, devices which are even more advanced than the ELCB, are available today.
7. After that, both the lines enter the MCB distribution board. We have already learned about MCB.
• It is a safety device which will break the circuit if there is any fault in the circuit. Details here.
• What we have now, is a 'MCB distribution board'. This board combines two functions:
(i) It helps to take out branches from the phase line
♦ Each of those branch will go into it's own circuit
♦ One such circuit will be available for each room in the house
(ii) It provides the 'circuit breaking safety' for each of those circuits
8. So, after branching at the 'MCB distribution board', we will get several 'live lines'. In our present case, we have 3 'live lines'.
• Each live line goes into it's own circuit.
• One such circuit is shown in detail. This circuit has 3 appliances:
a bulb, a fan and a 3 pin socket
9. These 3 appliances should be connected in parallel
• In the fig.12.6, they are indeed connected in parallel.
• If we have more space to draw, that circuit can be drawn as shown in fig.12.7 below:
 |
| Fig.12.7 |
• The reader may compare the switch board in fig.12.7 with that in fig.12.6 and verify that, they are the same.
• In fig.12.7, notice how 'an additional bulb taken from the 3 pin socket' will effectively complete the flow of current through the socket. The green line is the 'earth line'. We will see it's details in the next section.
■ The system shown in fig.12.6 is called the tree system.
Now we will see the kwh meter. We will write it in steps:
1. We have learned about 'electric power' (Details here)
• Consider an appliance on which it is marked as '1000 watts'
• That means, that appliance will consume an energy of 1000 joules in one second
2. If the consumer uses that appliance for one hour, how much energy will be used?
Ans: 1000 × 60 × 60 = 3600000 joules = 3600 kilo joules
• The consumer will have to pay money for this 3600 kilo joules
3. But the distribution companies do not measure energy in joules or kilo joules.
■ They use another unit: kilowatt hour
4. Let us see how this unit is derived:
• We know that 'power' is the ratio of Energy to time. That is:
Power = Energy⁄time
• Multiplying both sides by 'time', we get:
Power × time = Energy⁄time × time
5. But [Energy⁄time × time] = Energy
• Then (4) becomes: Power × time = Energy
• So, to get 'amount of energy used', we can multiply the following two quantities:
(i) Power of the appliance
(ii) Time for which the appliance is used
6. We can write:
Amount of energy used by an appliance
= Power of the appliance × Time for which the appliance is used
7. Based on this, we can derive 'units':
• unit of energy = unit of power × unit of time
⟹ unit of energy = watts × sec
8. For large values, we can use:
• kilowatts instead of watts (∵ 1000 watts make up one kilo watt)
• hour instead of sec (∵ 3600 seconds make up one hour)
■ So we get:
Unit of energy = kilowatt hour (kwh)
• This unit is used by the distribution companies.
9. The companies use the simple term: 'units'
■ 1 unit = 1 kwh
An example:
• If a consumer uses '25 units' of electricity, it means that, he uses 25 kwh of electrical energy
10. On many occasions, we will want to know the 'number of units' consumed in our homes and offices. So let us derive an easy method:
• The two information that we will be having are:
♦ Power of the appliance (in watts)
♦ Time for which the appliance is used (in hours)
• Based on the above two, we must be able to quickly find the 'number of units'. Let us try:
We will write the steps:
(i) When 'power' is multiplied by 'time', we get 'energy'.
• So '(watt × hour) = watt hour' is energy
(ii) But we want 'kilowatt hour'
• So we must divide 'watt hour' by 1000
• Then we will get 'kwh' or the 'number of units' directly.
(iii) We can write the formula:
Let us see an example:
Solved example 12.1
A grinder of power 750 W works for 2 hours. Calculate the energy consumed
Solution:
1. Given that, power = 750 W, Time = 2 hours
2. We have:
Substituting the values, we get:
Energy (kwh) = 750×2⁄1000 = 1.5 kwh = 1.5 units
Another method:
1. Given that, power = 750 W
So the grinder consumes 750 joules every second
2. In 2 hours, there are (2 × 3600) seconds
So energy consumed in 2 hours = 750 × 2 × 3600 = 5400000 joules
3. We have to convert this into kwh:
(i) 1 kilowatt = 1000 watts = 1000 joules per second
• 1 hour = 3600 seconds
(ii) So energy of 1 kwh = (1000 3600) = 3600000 joules
(iii) So 1 joule = 1⁄3600000 kwh
(iv) So 5400000 joules = (5400000 × 1⁄3600000) = (54⁄36) = 1.5 kwh
• The kwh meter is installed by the distribution companies.
• It directly shows the consumption in kwh
• So we need not calculate the consumption in joules
• Some images can be seen here.
Solved example 12.2
In a house, in a day,
• 5 CF lamps each of 20 W, work for 4 hours
• 4 fans each of 60 W, work for 5 hours
• 1 TV of 100 W, works for 4 hours
What will be the consumption shown by the kwh meter per day?
Solution:
1. Power consumption of 1 CF lamp = 20×4⁄1000 = 0.08 kwh
∴ Power consumption of 5 CF lamps = 0.08 × 5 = 0.4 kwh = 0.4 units
2. Power consumption of 1 fan = 60×5⁄1000 = 0.3 kwh
∴ Power consumption of 4 fans = 0.3 × 4 = 1.2 kwh = 1.2 units
3. Power consumption of 1 TV = 100×4⁄1000 = 0.4 kwh = 0.4 units
4. Total consumption = 0.4 + 1.2 + 0.4 = 2 units
In the next section, we will see the details of a 3 pin plug
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