Chapter 12.2 - Household Electric Circuits

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:

Fig.12.6

• 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: 

Fig.12.7

• 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.

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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:

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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

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• 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.

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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

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In the next section, we will see the details of a 3 pin plug

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Chapter 10.1 - Heating Coil and Safety Fuse

In the previous section we saw a special property of electricity:
■ Electricity will produce heat when it passes through a conductor. 
• We also saw how to calculate the 'quantity of heat' produced. 
• In this section, we will see two practical applications of this property.

I HEATING COILS
We will write the steps:
1. One of the most common reasons that we want to produce heat is while cooking food. We can cook food properly only if sufficient heat is available. 
• We can easily produce heat for this purpose by using a coil stove. See images of coil stoves here.    
2. On many occasions we will need to heat small or large quantities of water. 
• When a small quantity of water is to be heated, we can use a portable immersion type water heater. See images of such water heaters here.
3. A soldering iron is a small hand tool with a pointed tip. It is used to melt solder (a low melting alloy). 
• The molten solder can be used to fill the space between metallic parts in electric circuits. Thus those metallic parts will be joined together. See images of soldering iron here.

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• All the three examples given above use a 'heating coil' to produce heat. 
• When a current 'I' passes through a heating coil for a time 't' seconds, heat will be produced according to the Eq.10.1: H = I²Rt
• R is the resistance of the coil. 
• So it is clear that, to produce more heat, R should be high.
■ Usually Nichrome is used to make heating coils.
• Nichrome is an alloy of nickel, chromium, iron and manganese
■ Four properties possesed by nichrome, makes it suitable for making heating coils:
1. Nichrome has a very high resistivity (Details here)
• So the conductors made using nichrome will have a very high 'R' value
2. Nichrome has a very high melting point
• So nichrome will not melt even if large quantities of heat is produced in it 
3. Nichrome has the ability to remain in red hot condition for a long time with out getting oxidised
• When temperature is increased, even non-reactive materials may enter into chemical reactions with the atmospheric oxygen. But nichrome does not enter into such reactions even if temperature is high
4. Nichrome has a low expansion coefficient
• When temperature increases, metals and alloys tend to expand in size. But nichrome does not expand much.

II SAFETY FUSE
• Before seeing how the safety fuse works, we must first understand the situations when safety fuse becomes a necessity.
(a) Short circuit
1. A short circuit is an 'unwanted and dangerous circuit' inside a normal circuit. 
• Though it is unwanted, it some times occurs accidentally due to the defects in the wiring system.
2. 'Short' is opposite of 'long'. So 'short circuit' can be considered as the opposite of 'long circuit'. 
• A long circuit is the required normal circuit designed by engineers and technicians. 
• In that circuit, current flows through the required appliances like TV, refrigerator etc., 
3. But due to defects in the wiring, the positive and negative terminals come into direct contact with each other. 
• In such a situation, there will be 'no resistance' to the current flow.
• Instead of flowing through the appliances, the current will flow directly between the positive and negative terminals. 
4. Since there is no resistance between them, a large current will begin to flow. 
• The wires in the circuit are not designed to carry such large currents. 
• They will get heated, resulting in sparks and fire.
5. If the current flow can be stopped just when such high currents begin to flow, sparks and fire can be avoided

(b) Over loading  
1. When engineers and technicians design a circuit, they will specify the 'exact number and types' of appliances that can be connected in that circuit.
2. They will connect all heavy appliances together in a separate circuit
• More current will flow through such a circuit
• So the wires in that circuit will be 'special wires' which can carry such heavy currents
3. They will connect all normal appliances together in a separate circuit
• Less current will flow through such a circuit
• So the wires in that circuit will be 'normal wires' which need carry only normal currents
4. If somebody connects 'more appliances' or 'heavier appliances' to the existing circuits, more current will flow. This situation is called 'over loading'
• Even 'special wires' will not be able to carry such heavy currents. 
• They will get heated resulting in sparks and fire.
5. If the current flow can be stopped just when such high currents begin to flow, sparks and fire can be avoided

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■ So we see that, it is essential to stop the current just when short circuit or over loading occurs. 

• How does the safety fuse help us to achieve this objective? 
We will write the steps:
1. The fig.10.2 below show two types of 'fuse plugs' 
    ♦ 'Fuse plugs' are installed inside a 'fuse box'
    ♦ The 'fuse box' is connected in series to the circuit
2. Consider the larger fuse plug in the fig. There are two u-shaped metallic parts

Fig.10.2. Source: By Anihl - Own work, Public Domain, https://commons.wikimedia.org/w/index.php?curid=5001280

• To complete the circuit, current must be able to flow from one u-shaped portion to the other u-shaped portion. 
• But they are separated by an insulating material. 
• The only connection between them is a thin metallic wire. This metallic wire is called fuse wire
3. We have seen that, when a short circuit or overloading occur, heavy currents will begin to flow through the circuit.
• Since the fuse is connected in series, this heavy current will flow through the fuse wire also 
4. Now, the fuse wire has a special property: Low melting point
• Indeed a fuse wire should be made of materials having low melting points
• Also a fuse wire should be thin
• So special alloys are used for making them
5. When heavy current flows through the fuse wire, it will get heated up according to 
Eq.10.1: H = I²Rt.
• Since the melting point is low, the heat developed due to the heavy current is enough to melt it
6. When it melt, it will break apart. 
• So the current will no longer flow between the u-shaped metallic parts 
• Thus the current flow in the circuit is stopped
    ♦ The 'fuse box' should be connected in series to the circuit. Otherwise, the current will take an alternate path and it will not serve the purpose.

7. Even when the circuit is performing in a normal condition, some heat is generated in the fuse wire

• But this heat is small and is dissipated into the surroundings
• When the current flow becomes excess, more heat is developed, which cannot be dissipated. Then the fuse wire will melt
■ Thus we can write: Safety fuse is a device that works on the 'heating effect of electric current'. It protects the appliances from short circuit and overloading.
8. When a fuse wire is included in a household wiring, the following precautions should be taken:
• The ends of the fuse wire must be connected firmly at appropriate points
• The fuse wire should not project outside the carrier base
• Length of the fuse wire should not exceed the limit
• The fuse must be connected in series in the circuit

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In the next section we will see the 'lighting effect' of electric current

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