High school Physics Lessons: MCB

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.

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⁄_3600000kwh
(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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In the previous section we saw the current through a circular conductor. We also saw that, increasing the number of circular conductors will increase the strength of the magnetic field. In this section, we will see an activity to prove this.

1. Consider the circular conductor shown in fig.9.9(a) below.

Fig.9.9

• The two points at which it pierces through the cardboard are named as A and B.
• The conductor must be 'straight up'. That is., it must be perfectly vertical.
• Also the cardboard must be perfectly horizontal.
2. The line through A and B should be aligned exactly in the North-South direction
3. The exact midpoint between A and B is named as C
• Through C, a perpendicular line XY is drawn
4. Place a magnetic needle exactly centred at C. This is shown in fig.b
[Note that, the magnetic needle should be mounted on a pivot. Then only it will rotate freely. In the fig. however, the pivot is not shown. Also the connections of the conductor to the battery is not shown in the fig. These are to avoid clutter and thus increase clarity]
5. Now we can turn on the switch. The current flows from A to B. This is shown in fig.9.10(a) below:

Fig.9.10

• The needle deflects towards the west.
■ This is due to the force exerted by the circular conductor
6. Now gradually move the needle towards X.
• The movement should be along the line XY
• We can see that the deflection gradually decreases.
♦ The needle is moving back towards the normal North-South orientation.
• This is because, as the distance from the conductor increases, the force exerted by it decreases.
7. Keep moving the needle.
• We will reach a particular point at which the needle is back in the exact North-South orientation.
8. Mark this point as O₁. This is shown in fig.9.11(a) below:

Fig.9.11

• Measure the distance CO₁ and note it down.
■ We can write: Beyond the point O₁, the conductor has no influence on the needle
9. Turn off the switch. Add a second circular conductor parallel to AB. This is shown in fig.b. Repeat the experiment.
• Ensure that the current I is same as that in the previous trial. This can be done using a rheostat.
[It is important to ensure that the currents are the same. Because, we want to prove that, the magnetic field becomes stronger because of an additional conductor. It must not be due to the increase in current]
• Find the point O₂ and mark it.
• O₂is the point beyond which, the 'combined action the two circular conductors' have no influence on the needle.
10. Measure the length of CO₂and note it down
• We will see that, CO₂ is greater than CO₁
■ This is because, the combined action produced a stronger magnetic field. This stronger magnetic field can exert a force to a greater distance.
• If we add a third circular conductor, even if the current is the same, we will find that CO₃ is greater than CO₂

So we achieved our objective. We proved that:
■ Increasing the number of circular conductors will increase the strength of the magnetic field.
• But now a problem arises:
We need to figure out a method to connect those circular conductors together. Then only the 'same current from a single battery source' will flow through them.
• Consider the conductor in fig.9.12(a) below:

Fig.9.12

• The current flowing upwards through end X will come downwards through the end Y.
♦ This is possible because the conductor is wound in the form of a spring coil.
• This coil can be made to pierce through a cardboard. It is shown in fig (b).
• When we look from above the cardboard, it will appear as two separate circular conductors.
♦ But there is interconnection below the card board.
• If we want three circular conductors, one more turn can be added to the coil. This is shown in fig.9.13 below:

Fig.9.13

• In fact we can add a large number of turns. This is shown in fig.9.14 below:

Fig.9.14

■ When the 'number of turns' of the coil is increased, the strength of the magnetic field is increased.
• Such a coil is indeed used in many electrical devices. It is called a solenoid.
Some images can be seen here.
• It is used in situations where a strong magnetic field is required.
■ The official definition is:
Solenoid is a conducting coil wound in the shape of a spring.

• We know that each individual turn of the solenoid will have it's own magnetic field.
• So the fields of adjacent turns will combine together to give a strong magnetic field
• The fig.9.15 below shows a comparison between the following two items:
(a) The magnetic field lines around a solenoid
(b) The magnetic field lines around a bar magnet

Fig.9.15

• The details of the solenoid in the above fig. is obtained from wikimedia commons here
• The details of the bar magnet in the above fig. is obtained from wikimedia commons here
■ Comparing the two, we can see that, they are identical.
That is.,
• The magnetic field lines around a solenoid
Is identical to:
• The magnetic field lines around a bar magnet

So a current carrying solenoid will act as a bar magnet. Our next task is to find it's poles
There are 3 methods to find the poles. They are described below:
Method 1:
• Bring a magnetic needle near one end of the current carrying solenoid
♦ If the north pole of the needle gets attracted, then that end of the solenoid is it's south pole
♦ If the south pole of the needle gets attracted, then that end of the solenoid is it's north pole
Method 2:
We will write this method in steps:
1. Consider the solenoid in fig.9.16 (a) below:

Fig.9.16

• The current goes up through X and comes down through Y
2. Imagine we are standing at the tail end of the cyan arrow. And we are looking towards the head end of the cyan arrow
• We will see that, the current I is flowing in the clockwise wise direction
3. Imagine we are standing at the tail end of the red arrow. And we are looking towards the head end of the red arrow
• We will see that, the current I is flowing in the anti-clockwise wise direction
4. The opposite of the above two will happen when the current is reversed. This is shown in fig.b
• At end X, the the current is flowing in the anti-clockwise direction.
• And at end Y, the current is flowing in the clockwise direction.
5. So we find an important property:
■ Even if current is flowing normally from one end of the solenoid to the other end, when looked from either ends, one is clockwise and the other is anti-clockwise.
• This property can be related to the polarity. The rule is:
(i) Hold a solenoid against your face.
(ii) Note the direction of current at the end nearest to your face.
• If the direction is clockwise, then that end is the south pole.
• If the direction is anti-clockwise, then that end is the north pole.
Method 3:
1. Consider the solenoid in the above fig.9.16(a).
• Imagine that the following two conditions are satisfied:
(i) You are holding it in the right hand.
(ii) The thump is pointing towards the end X.
2. If the above two conditions are satisfied, the other fingers will be pointing in a 'direction opposite to the direction of current'.
• Such an 'opposite pointing' is not allowable for this method to work
• We want 'pointing in the same direction'. So what do we do?
3. Note that, only right hand should be used. Let the thumb point towards Y. We will write the steps again:
• Imagine that the following two conditions are satisfied:
(i) You are holding it in the right hand.
(ii) The thump is pointing towards the end Y.
4. If the above two conditions are satisfied, the other fingers will be pointing 'in the same direction of current'.
• So this is acceptable.
• In this situation, the end towards which the thumb points is the north pole.
So we can write a summary of this third method:
■ Imagine the solenoid being held by the right hand. If the four fingers encircling the solenoid shows the direction of the current, the thumb indicates the north pole.

So we have seen the basic properties of a solenoid. Now we will see methods to increase the magnetic strength of a solenoid.
Method 1:
• We know that the solenoid has a large number of turns.
• We have also seen that, when current is turned on, 'a combination of magnetic fields' of the individual turns takes place.
• So if the 'number of turns' is increased, the strength of the magnetic field will increase.
Method 2:
• Use a soft iron core. Let us see how it is done:
• We know that the solenoid has a large number of turns.
• If these turns are made around a soft iron core, then the strength of the magnetic field will increase. This is shown in the fig.9.17 below:

Fig.9.17 Source: Wikimedia commons

■ The following properties of soft iron makes it suitable for the core:
• It has greater magnetic susceptibility
♦ That is., soft iron is 'attracted more' into a magnetic field than other metals
• It has greater magnetic permeability
♦ That is., soft iron has a greater 'tendency to support the formation of magnetic fields within it's body' than other metals

Now we will see the working of a Miniature Circuit Breaker, which is commonly known as MCB.

We will write it in steps:
1. In the fig.9.18(a) below, for the bulb to glow, current must flow from A to B.

Fig.9.18

2. But between A and B, a MCB is placed.
• The cyan rectangle shows the body of the MCB.
• The circuit will be complete only if the current successfully come out of the MCB.
3. The current entering the MCB is lead to the coil shown in red colour.
• So the current flows through all the turns of the coil.
• A soft iron core is placed inside the coil.
• The current emerging from the coil passes through the conductor shown in green colour.
• After passing through the green conductor, the current emerges from the MCB and flows into the bulb. Thus the circuit is completed.
4. But when there is a fault in the circuit as shown in fig.b, or when there is an over load, excess current flows through the circuit.
• Then a strong magnetic field is developed in the coil.
• The soft iron core will get magnetized. That is., the soft iron core will become a temporary magnet.
• So it will be attracted towards the green conductor. Because of the forward motion of the soft iron core, the green conductor will be displaced from it's original position.
• Thus the circuit will break. Current will no longer flow through the circuit.

In the next section we will see some basics about the Electric motor.

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High school Physics Lessons

Pages

Saturday, June 16, 2018

Chapter 12.2 - Household Electric Circuits

Wednesday, May 2, 2018

Chapter 9.2 - The Solenoid