Slide – Exercise 11 – Motors and Generators




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#1 Maximum Torque | Direction of Magnetic Field | Law of Conservation of Energy

An electric DC motor consists of 500 tons of wire formed into a 20 centimetre by the 10-centimetre rectangular coil. The coil is in a field of one millimetre, and a current of four amps flows through it. What is the maximum torque? And when does the coil experience it?
So, it wants to this question, we need to remember our equation for torque. Can you remember what it is? That's right, torque equals (n)(b)(i)(a) (cos θ). Right. Now, if we want cosine to be a maximum, that means that we want theta to be zero, right?
So, we know that our cosine is going to need to be parallel to the field, which means that our only options are A and C. In order to figure out the magnitude, all we have to do is substitute in b, i and a. And so, by doing that, we end up with an answer of 0.04 Newton meters.
Question 2: Wires placed on top of the pole of a disc magnet as shown. So, we can see the flat surface of the magnet will be either the North Pole or the South Pole. The wires connect to a battery and experiences of force in the direction shown by the arrow.
Right, so we either have current flowing from x toy, or from y to x. So, one of the directions of the magnetic field and the current, we have two options for the field, the field is vertically upwards or in the direction of the arrow. Now because we know that the face of the magnet, that is the top is either the North Pole or the South Pole, we know that we can't have the field going across it in the direction of the arrow. Right?
So the only option is that the field is vertically upwards. Right? So, we might draw something like this coming out of the top of the magnet, right? There's a magnetic field. Now in order to figure out the direction of the current, we need to use our right-hand rule. Okay, so the magnetic field points upwards. And the force of the wire experiences points in that direction, which means that the current must be flowing from x to y. So, A is our correct answer.
Don't forget to always use your right hand with the right-hand rule. If you're using your right hand to hold a pencil or a pen, and you use your left hand instead, you'll get the wrong answer.
Question 3: An electromagnet is attached to the bottom of a light train. When a large current is passed through the electromagnet, the train slows down as a direct result of the law of conservation of energy. Now, which one of the following devices is the law of conservation of energy applied in the same way.
So, what's happening when the train slows down is that the changing magnetic field passing through the wheels is causing the wheel to try and stop moving in relation to that magnetic field. Right and so they slow down. Now in these four options, there's only one option in which something tries to keep up with a magnetic field. And that one is, of course, the induction motor.
In the induction motor, instead of a stationary magnetic field, we have a rotating magnetic field. And so, in order to allow conservation of energy to happen, the rotor inside the motor has to turn around at the same rate as the field. Otherwise, we would get electrical energy out of nowhere. Just like we would get electrical energy out of nowhere. If these wheels didn't slow down, because we would have a conductor in a changing magnetic field.

#2 Lenz's Law | Split-Ring Commutator | DC Electric Power

In which of the following statements best describes Lenz's law, we have a few options, a current-carrying wire produces a magnetic field. The induced emf is proportional to the rate of change of magnetic flux, the direction of the induced emf opposes the change that creates it, or changing electric field produces a changing magnetic field.
Now, remember, Lenz's law allows us to figure out the direction of induced current, or indeed, induced magnetic field. Remember that the way that we figure it out, is by remembering that the field created by Lenz's law will always oppose the ones that create them, they'll try to make your life harder. And so, the best statement of that is B. Or C rather, the direction of the induced EMF opposes the field that created right? So, this is a statement of Lenz's law.
Question 5: Which of the following options correctly describes the function of the split ring commutator in a DC generator? Does it ensure the current external circuit always points in the same direction? Does it ensure the current through the generator coils always flows in the same direction? Does it change the direct current produced by the coil into alternating current? Or does it ensure the torque on the coils always stays in the same direction?
Now, two of these options at first might seem familiar. That's B and D. But both of these only work for DC motors. Right? The commutator can't change the current that's going through the coil. Because the current through the coil is what's being created and needs to be put into the external circuit. That means that our correct answer is going to be A and it shows that the current to the external circuit always goes in the same direction.
Question 6: Despite my proposition in the 1800s ac electrical power has become preferred to DC electrical power. Why? Is it because motors require AC to operate, AC is safer than DC, the voltage of an AC signal can be changed, or because electrical devices that use AC are more efficient?
Now, we know from our studies on motors that we can build motors to operate either on DC power or an AC power, so it can ruin A straightaway. AC is not in fact, safer than DC at high voltages, it's a little more dangerous. Because of the way alternating current can interfere with muscles of the heart. Electrical devices that use AC are in fact a little less efficient, especially if they transform the AC signal because they'll lose energy in eddy currents.
But the huge advantage of AC power is that we can use it in transformers. And transformers of course change the voltage. So, the big advantage of AC power compared to DC power is that the voltage of the signal can be changed. And if we want to have devices that use different voltages, we don't need to have a number of different DC generators.

#3 Primary Coil | Secondary Coil | Transformer Coil

A transformer has 200 tons of wire in its primary coil, and 1500 tons in its secondary coil, an AC signal 50 volts is applied to the primary coil, what is the output voltage of the secondary coil?

So, to figure this one out, all we need to do is remember the ratio of the number of turns in each coil is the same as the ratio of the voltages. Right? So, v1 over v2 equals n1 over n2. Yeah. And so, in this case, n1 will be 200 and n2 will be 1500. So, if the AC signal 50 volts is supplied to the primary coil, v1 then v2 is going to be 375 volts. Makes sense, right? You can substitute in the numbers yourself if you do not believe me.

Question 8: An ideal transformer converter 240-volt signal into a 12-volt DC signal, the power used by the slot cars is 60 watts, which of course will be the same as voltage times current. If there are 100 times in the secondary coil, find a number of times in the primary coil and the current flowing through the primary coil. Alright.

So, we can see from the options that either we are going to get the number of turns being larger or smaller in the same ratio as the voltages, and the current is going to be larger or smaller in the same ratio as the voltages, right? So, what we need to figure out is how the number of turns in the primary coils differs and how the current in the primary coils differs.

Now another number of turns is going to be the same as the ratio of the voltages. Yeah, so if we have a very large signal being transformed into a small signal, that means that there is going to be a large number of times in the primary coil and a small number of times in the secondary coil. So, our choice is either A or C right.

We also know that if the amount of power in each set of coils is constant 60 watts, then we should be able to use that to figure out how the current will change because power is voltage times current right. Now, if we have a high voltage being transformed into a low voltage, but the power 60 watts stays the same. That means that the high current– sorry the low voltage will need a high current and the high voltage will need a low current. Right. So, the primary coil is high voltage, so it has lots of turns and low current. Our answer then is going to be 2000 turns and 0.25 amps.

Question 9: Which transform will be able to step down an AC voltage from 240 volts to six volts. To answer this question, we just need to look at the ratio of the voltages 240 to 6 is the same as 40 to 1 or the same as which one of these, that is right 480 to 12. So, this is the correct answer.

#4 Secondary Voltage | Slip Rings

A transformer has a primary coil with 60 turns, and a secondary coil with 2300 turns. If the primary voltage in the transformer is 110 volts, what is the secondary voltage? Is it 2.4 times 10 to the minus four 2.4 times 10 to the to 1.3 times 10 to the three, or 4.2 times 10 to the 3?
So, remember to answer this one, once again, all you need to do is use our equation for the voltages in a transformer, v1 to v2 equals n1 over n2. Right? So, if our turns are 60 and 2300, then our voltages will be in that same ratio. Right? So, if the secondary coil has more turns, it will have more voltage. And the ratio tells us that our answer is going to be 4.2 times 10 to the three volts that is 4200 volts.
Question 11: What is the function of the slip rings on an AC motor, not an AC generator, is it to change the direction of the supply current flowing into the coil, to provide electrical contacts between the coil and the external circuit to provide a constant magnitude torque on the coil or to change the direction of the torque on the coil every half revolution.
Now if we have a motion, we do not want to change the direction of the torque on the coil, right that would result in the motor stops. So, it is not going to be D. We also know that we are not going to change the direction of the supply card because that is already changing, so it will not be A, right. If we provide a constant magnitude torque on the coil, then we would need to have a motor that does not use slip rings. We need perhaps a squirrel cage motor. In an AC motor that uses slip rings, we do not get constant torque. The only remaining is B, to provide electrical contacts between the coil and the external circuit. That is all the slip rings do.
Question 12: Which option best describes the difference between the structure of a motor and the structure of a generator. Other sources of power, the commutator, the brushes, or the magnetic field different well we know that we can construct both of these with a permanent magnetic field is pointing one direction. So, the magnetic fields can be the same. The brushes can be the same and so can the compensate because these just provide contact between the external circuit and the coil. Right? Whether that coil is receiving electricity or producing electricity.
But therein lies the actual difference. One of the coils produces electricity and the other one receives electricity from an external source. So, in both cases, the sources of power are different. In a motor, the source of power is the electricity that is being used to turn the coil. But in a generator, the coil is sort of turned by hand and the electricity is pushed out by that.

#5 Back emf | Eddy Current Brake | Iron Core

A motor with an internal resistance of 100 ohms is connected to a 12-volt power supply and draws 20 milliamps of current. So, what back emf does it produce?
To answer this question, we need to figure out the effective voltage across the coil, right. Voltage equals current times resistance. Current is 20 milliamps resistance is 100 ohms. So, by multiplying these together, we can figure out the voltage across the coil 0.002 amps times 100 ohms gives us two volts right.
So, we have only two volts of voltage across the coil. If our 12-volt power supply is only producing two volts, that means there must be a back emf of 10 volts. So, d is the correct answer.
Question 14: What is the net energy transformation that takes place in an Eddy current braking system? Is its kinetic energy to electrical energy, kinetic energy to heat energy, kinetic energy to magnetic energy or kinetic energy to potential energy?
So, let us think about this. We obviously start with kinetic energy because we're starting with something moving and we are ending up with something stopped, right. Now, when the moving wheels of the thing pass through a magnetic field, then eddy currents will be produced that will slow the wheels down. Right. So that means we are turning kinetic energy and turning into electrical energy.
But the transformation is not finished yet. Because these are eddy currents with nowhere else to flow, they dissipate due to the resistance of the metal and become heat energy. So, the net energy transformation that is the total energy transformation that happens over time is not kinetic energy into electrical energy, but kinetic energy into heat energy. Which by an interesting coincidence, is the same transformation as occurs in regular breaks that use friction.
Question 15: What is the purpose of laminating the iron core of a transformer? Is it to increase the flux passing through the coils of the transformer, to decrease the weight of the transformer, to decrease the cost of the transformer or to decrease the eddy currents induced in the transformer?
Now the purpose of the iron core itself is to increase the flux passing through the cause of the transformer. Right. But that is not what the question is asking, it is saying what is the purpose of eliminating the iron core? That is dividing into lots of little slices and putting insulators between those slices?
The answer, of course, is to decrease the eddy currents induced in the transformer. If we do not have a laminated core, then the eddy currents in the core can be quite large and we can lose a lot of energy that way. If we eliminate it, then we do not decrease the magnetic flux passing through it. But we do decrease the potential for eddy currents. So, by eliminating the core, we can make it a lot more efficient.