DC motors
A simple DC motor has a coil of wire that can rotate in a magnetic field. The current in the coil is supplied via two brushes that make moving contact with a split ring. The coil lies in a steady magnetic field . The forces exerted on the current-carrying wires create a torque on the coil.
The force F on a wire of length L carrying a current i in a magnetic field B is iLB times the sine of the angle between B and i, which would be 90° if the field were uniformly vertical. The direction of F comes from the right hand rule, as shown here. The two forces shown here are equal and opposite, but they are displaced vertically, so they exert a torque. (The forces on the other two sides of the coil act along the same line and so exert no torque.)
The coil can also be considered as a magnetic dipole, or a little electromagnet, as indicated by the arrow NS: curl the fingers of your right hand in the direction of the current, and your thumb is the North pole. In the sketch at right, the electromagnet formed by the coil of the rotor is represented as a permanent magnet, and the same torque (North attracts South) is seen to be that acting to align the central magnet.
Note the effect of the brushes on the split ring. When the plane of the rotating coil reaches horizontal, the brushes will break contact (nothing is lost, because this is the point of zero torque anyway--the forces act inwards). The angular momentum of the coil carries it past this break point and the current then flows in the opposite direction, which reverses the magnetic dipole. So, after passing the break point, the rotor continues to turn anticlockwise and starts to align in the opposite direction. In the following text, I shall largely use the 'torque on a magnet' picture, but be aware that the use of brushes or of AC current can cause the poles of the electromagnet in question to swap position when the current changes direction.
The torque generated over a cycle varies with the vertical separation of the two forces. It therefore depends on the sine of the angle between the axis of the coil and field. However, because of the split ring, it is always in the same sense. The animation below shows its variation in time, and you can stop it at any stage and check the direction by applying the right hand rule.
Motors and generators
Now a DC motor is also a DC generator. Have a look at the next animation. The coil, split ring, brushes and magnet are exactly the same hardware as the motor above, but the coil is being turned, which generates an emf.
If you use mechanical energy to rotate the coil (N turns, area A) at uniform angular velocity w in the magnetic field B, it will produce a sinusoidal emf in the coil. Let q be the angle between B and the normal to the coil, so the magnetic flux f is NAB.cos q. Faraday's law gives:
emf = - df/dt = -(d/dt) (NBA cos q)
= NBA sin q (dq/dt) = NBAw sin wt.
The animation above shows what is called a DC generator. As in the DC motor, the ends of the coil connect to a split ring, whose two halves are contacted by the brushes. Note that the brushes and split ring 'rectify' the emf produced: the contacts are organised so that the current will always flow in the same direction, because when the coil turns past the dead spot, where the brushes meet the gap in the ring, the connections between the ends of the coil and external terminals are reversed. The emf here (neglecting the dead spot) is |NBAw sin wt|, as sketched.
An alternator
If we want AC, we don't need recification, so we don't need split rings. (This is good news, because the split rings cause sparks and extra wear. If you want DC, it is often better to use an alternator and rectify with diodes.)
In the next animation, the two brushes contact two continuous rings, so the two external terminals are always connected to the same ends of the coil. The result is the unrectified, sinusoidal emf given by NBAw sin wt, which is shown in the next animation.
This is an AC generator. The advantages of AC and DC generators are compared in a section below. We saw above that a DC motor is also a DC generator. Similarly, an alternator is also an AC motor. However, it is a rather inflexible one. (See How real electric motors work for more details.)
Back emf
Now, as the first two animations show, DC motors and generators may be the same thing. For example, the motors of trains become generators when the train is slowing down: they convert kinetic energy into electrical energy and put power back into the grid. Recently, a few manufacturers have begun making cars rationally. In such cars, the electric motors used to drive the car are also used to charge the batteries when the car is stopped - it is called regenerative braking.
So here is an interesting corollary. Every motor is a generator. This is true, in a sense, even when it functions as a motor. The emf that a motor generates is called the back emf. The back emf increases with the speed, because of Faraday's law. So, if the motor has no load, it turns very quickly and speeds up until the back emf, plus the voltage drop due to losses, equal the supply voltage. The back emf can be thought of as a 'regulator': it stops the motor turning too quickly. When the motor is loaded, then the phase of the voltage becomes closer to that of the current (it starts to look resistive) and this apparent resistance gives a voltage. So the back emf required is smaller, and the motor turns more slowly. (To add the back emf, which is inductive, to the resistive component, you need to add voltages that are out of phase. See AC circuits.)
A simple DC motor has a coil of wire that can rotate in a magnetic field. The current in the coil is supplied via two brushes that make moving contact with a split ring. The coil lies in a steady magnetic field . The forces exerted on the current-carrying wires create a torque on the coil.
The force F on a wire of length L carrying a current i in a magnetic field B is iLB times the sine of the angle between B and i, which would be 90° if the field were uniformly vertical. The direction of F comes from the right hand rule, as shown here. The two forces shown here are equal and opposite, but they are displaced vertically, so they exert a torque. (The forces on the other two sides of the coil act along the same line and so exert no torque.)
The coil can also be considered as a magnetic dipole, or a little electromagnet, as indicated by the arrow NS: curl the fingers of your right hand in the direction of the current, and your thumb is the North pole. In the sketch at right, the electromagnet formed by the coil of the rotor is represented as a permanent magnet, and the same torque (North attracts South) is seen to be that acting to align the central magnet.
Note the effect of the brushes on the split ring. When the plane of the rotating coil reaches horizontal, the brushes will break contact (nothing is lost, because this is the point of zero torque anyway--the forces act inwards). The angular momentum of the coil carries it past this break point and the current then flows in the opposite direction, which reverses the magnetic dipole. So, after passing the break point, the rotor continues to turn anticlockwise and starts to align in the opposite direction. In the following text, I shall largely use the 'torque on a magnet' picture, but be aware that the use of brushes or of AC current can cause the poles of the electromagnet in question to swap position when the current changes direction.
The torque generated over a cycle varies with the vertical separation of the two forces. It therefore depends on the sine of the angle between the axis of the coil and field. However, because of the split ring, it is always in the same sense. The animation below shows its variation in time, and you can stop it at any stage and check the direction by applying the right hand rule.
AC motors
With AC currents, we can reverse field directions without having to use brushes. This is good news, because we can avoid the arcing, the ozone production and the ohmic loss of energy that brushes can entail. Further, because brushes make contact between moving surfaces, they wear out.
The first thing to do in an AC motor is to create a rotating field. 'Ordinary' AC from a 2 or 3 pin socket is single phase AC--it has a single sinusoidal potential difference generated between only two wires--the active and neutral. (Note that the Earth wire doesn't carry a current except in the event of electrical faults.) With single phase AC, one can produce a rotating field by generating two currents that are out of phase using for example a capacitor. In the example shown, the two currents are 90° out of phase, so the vertical component of the magnetic field is sinusoidal, while the horizontal is cosusoidal, as shown. This gives a field rotating counterclockwise.
(* I've been asked to explain this: from simple AC theory, neither coils nor capacitors have the voltage in phase with the current. In a capacitor, the voltage is a maximum when the charge has finished flowing onto the capacitor, and is about to start flowing off. Thus the voltage is behind the current. In a purely inductive coil, the voltage drop is greatest when the current is changing most rapidly, which is also when the current is zero. The voltage (drop) is ahead of the current. In motor coils, the phase angle is rather less than 90°, because electrical energy is being converted to mechanical energy.)
In this animation, the graphs show the variation in time of the currents in the vertical and horizontal coils. The plot of the field components Bx and By shows that the vector sum of these two fields is a rotating field. The main picture shows the rotating field. It also shows the polarity of the magnets: as above, blue represents a North pole and red a South pole.
If we put a permanent magnet in this area of rotating field, or if we put in a coil whose current always runs in the same direction, then this becomes a synchronous motor. Under a wide range of conditions, the motor will turn at the speed of the magnetic field. If we have a lot of stators, instead of just the two pairs shown here, then we could consider it as a stepper motor: each pulse moves the rotor on to the next pair of actuated poles. Please remember my warning about the idealised geometry: real stepper motors have dozens of poles and quite complicated geometries!
With AC currents, we can reverse field directions without having to use brushes. This is good news, because we can avoid the arcing, the ozone production and the ohmic loss of energy that brushes can entail. Further, because brushes make contact between moving surfaces, they wear out.
The first thing to do in an AC motor is to create a rotating field. 'Ordinary' AC from a 2 or 3 pin socket is single phase AC--it has a single sinusoidal potential difference generated between only two wires--the active and neutral. (Note that the Earth wire doesn't carry a current except in the event of electrical faults.) With single phase AC, one can produce a rotating field by generating two currents that are out of phase using for example a capacitor. In the example shown, the two currents are 90° out of phase, so the vertical component of the magnetic field is sinusoidal, while the horizontal is cosusoidal, as shown. This gives a field rotating counterclockwise.
(* I've been asked to explain this: from simple AC theory, neither coils nor capacitors have the voltage in phase with the current. In a capacitor, the voltage is a maximum when the charge has finished flowing onto the capacitor, and is about to start flowing off. Thus the voltage is behind the current. In a purely inductive coil, the voltage drop is greatest when the current is changing most rapidly, which is also when the current is zero. The voltage (drop) is ahead of the current. In motor coils, the phase angle is rather less than 90°, because electrical energy is being converted to mechanical energy.)
In this animation, the graphs show the variation in time of the currents in the vertical and horizontal coils. The plot of the field components Bx and By shows that the vector sum of these two fields is a rotating field. The main picture shows the rotating field. It also shows the polarity of the magnets: as above, blue represents a North pole and red a South pole.
If we put a permanent magnet in this area of rotating field, or if we put in a coil whose current always runs in the same direction, then this becomes a synchronous motor. Under a wide range of conditions, the motor will turn at the speed of the magnetic field. If we have a lot of stators, instead of just the two pairs shown here, then we could consider it as a stepper motor: each pulse moves the rotor on to the next pair of actuated poles. Please remember my warning about the idealised geometry: real stepper motors have dozens of poles and quite complicated geometries!
Motors and generators
Now a DC motor is also a DC generator. Have a look at the next animation. The coil, split ring, brushes and magnet are exactly the same hardware as the motor above, but the coil is being turned, which generates an emf.
If you use mechanical energy to rotate the coil (N turns, area A) at uniform angular velocity w in the magnetic field B, it will produce a sinusoidal emf in the coil. Let q be the angle between B and the normal to the coil, so the magnetic flux f is NAB.cos q. Faraday's law gives:
emf = - df/dt = -(d/dt) (NBA cos q)
= NBA sin q (dq/dt) = NBAw sin wt.
The animation above shows what is called a DC generator. As in the DC motor, the ends of the coil connect to a split ring, whose two halves are contacted by the brushes. Note that the brushes and split ring 'rectify' the emf produced: the contacts are organised so that the current will always flow in the same direction, because when the coil turns past the dead spot, where the brushes meet the gap in the ring, the connections between the ends of the coil and external terminals are reversed. The emf here (neglecting the dead spot) is |NBAw sin wt|, as sketched.
An alternator
If we want AC, we don't need recification, so we don't need split rings. (This is good news, because the split rings cause sparks and extra wear. If you want DC, it is often better to use an alternator and rectify with diodes.)
In the next animation, the two brushes contact two continuous rings, so the two external terminals are always connected to the same ends of the coil. The result is the unrectified, sinusoidal emf given by NBAw sin wt, which is shown in the next animation.
This is an AC generator. The advantages of AC and DC generators are compared in a section below. We saw above that a DC motor is also a DC generator. Similarly, an alternator is also an AC motor. However, it is a rather inflexible one. (See How real electric motors work for more details.)
Back emf
Now, as the first two animations show, DC motors and generators may be the same thing. For example, the motors of trains become generators when the train is slowing down: they convert kinetic energy into electrical energy and put power back into the grid. Recently, a few manufacturers have begun making cars rationally. In such cars, the electric motors used to drive the car are also used to charge the batteries when the car is stopped - it is called regenerative braking.
So here is an interesting corollary. Every motor is a generator. This is true, in a sense, even when it functions as a motor. The emf that a motor generates is called the back emf. The back emf increases with the speed, because of Faraday's law. So, if the motor has no load, it turns very quickly and speeds up until the back emf, plus the voltage drop due to losses, equal the supply voltage. The back emf can be thought of as a 'regulator': it stops the motor turning too quickly. When the motor is loaded, then the phase of the voltage becomes closer to that of the current (it starts to look resistive) and this apparent resistance gives a voltage. So the back emf required is smaller, and the motor turns more slowly. (To add the back emf, which is inductive, to the resistive component, you need to add voltages that are out of phase. See AC circuits.)
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