Electric Motor: Physics, Efficiency & Types

Q: How to calculate electric motor power?

Electric motor power can be calculated by measuring the time taken to do a known quantity of work . For example, lifting a 5N weight by 1m requires 5J of work. If the motor performs this work in 2 seconds, the output power can be calculated as 5J / 2S = 2.5W. Alternatively, if the output shaft torque and rotation speed can be measured, mechanical power can also be calculated as: Power = torque x rotational velocity , where torque is measured in Nm and rotational velocity in radians per second .

Q: What is the science behind electric motors?

Electric motors utilise the motor effect , which produces a force on a current carrying wire in a magnetic field. In a DC motor, a coil of wire is used so that each side experiences an opposite direction force in the magnetic field, causing the coil to rotate. Every half-turn, a split ring commutator flips the voltage polarity on the coil, reversing the current direction. Fleming’s left hand rule shows that this reverses the direction of the forces on the coil, ensuring it continues to be rotationally accelerated. Brushes are used to transfer the DC power supply to the rotating split-ring commutator.

Q: What is electric motor and its efficiency?

The electric motor is an electro-mechanical device which converts input electric power to output mechanical power. To calculate efficiency, the proportion of input energy that is converted to useful output work must be calculated using the following equation: Efficiency = (Useful output power) / (Input Power) Which can also be represented as: Efficiency = (Useful Mechanical Power) / (Electrical Power)

Q: How does an electric motor work?

Electric motors utilise the motor effect , which produces a force on a current carrying wire in a magnetic field. In a DC motor, a coil of wire is used so that each side experiences an opposite direction force in the magnetic field, causing the coil to rotate. Every half-turn, a split ring commutator flips the voltage polarity on the coil, reversing the current direction. Fleming’s left hand rule shows that this reverses the direction of the forces on the coil, ensuring it continues to be rotationally accelerated. Brushes are used to transfer the DC power supply to the rotating split-ring commutator.

Electric Motor Definition

An Electric motor is an electro-mechanical device that converts an electrical energy input to mechanical energy output. In DC motors this is achieved primarily through the interaction of a stationary magnetic stator and an electromagnetic rotor producing a force, this is known as the motor effect.

A wire carrying a current generates a magnetic field around the wire. When this electromagnetic field interacts with another magnetic field, created by a permanent magnet or electromagnet, a force is produced on the wire.

The amount of force depends on the strength of the permanent magnetic field, the length of the wire passing through the field and the amount of current, defined by the motor effect equation. The motor effect is strongest when the wire/current and magnetic field are at 90° to each other, with the effect strength decreasing to zero if the wire and magnetic field are parallel.

Electric Motors, Diagram showing the Motor Effect and the Fleming Left Hand Rule, StudySmarter (Left) Diagram of the motor effect, showing the interaction of a current-carrying wire with a magnetic field producing a force on the wire. (Right) Fleming’s left-hand tool - a method for determining the direction of the force on the wire. StudySmarter Originals.

$F = B \times I \times L$

$F$ is the force in newtons $(N)$

$B$ is the magnetic flux density in tesla $(T)$

$I$ is the current in ampere $(A)$

$L$ is the conductor length in meters $(m)$

Fleming's Left Hand Rule

Fleming’s Left-Hand Rule is a simple tool that can be used to easily work out the direction of force acting on a current-carrying wire in a magnetic field. Using your left hand, hold your thumb, index finger, and middle finger at right angles to each other, as shown above. Then, point your index finger in the direction of the magnetic field (north to south) and your middle finger in the direction of the current (+ to -). Your thumb then points in the direction of the resulting force on the wire!

Types of Electric Motors

There are countless different variations of an electric motor design for various applications, but they fall into two main classifications: Alternating current (AC) motors and direct current (DC) motors.

DC Motors

The simplest form of DC motor consists of a stationary magnetic field and a conductor coil connected to a split ring commutator, which is connected to a DC power supply via brushes. The diagram below shows this type of motor in a starting position.

Electric Motors Simple DC Motor Diagram StudySmarter Diagram showing components of a very simple DC motor, and how these create a rotational force around the motor axis. Ross MacDonald, StudySmarter Originals.

Now, let's take a look at how a DC motor works step by step:

As a voltage is applied to the brushes, the split ring commutator passes this voltage to the coil which creates a current on the coil. The current-carrying coil is in a magnetic field, so the motor effect produces an opposite force on each side of the coil as the current is travelling in opposite directions. This creates a rotational force on the coil, and in this example the motor begins to rotate anticlockwise.
After rotating by 90 degrees from the starting position, the split ring commutator reverses the direction of the current. This causes the side of the coil at the top of the rotation to now experience a force downwards, and the side of the coil at the bottom of the motor to experience a force upwards. Combined with the momentum from the initial rotation, this continues to accelerate the coil in an anticlockwise rotation.
After rotating a further 180°, the split ring commutator again reverses the current direction and changes the direction of the forces on the coil. This accelerates the coil through the next half-turn, and this sequence continues as the motor spins.

The split ring commutator is used to reliably switch the current direction in the coil at the same rate as the motor rotates. As can be seen in the diagram above, the split-ring commutator comprises of two half-cylindrical conductors that are attached to each end of the motor coil. Brushes conduct current from the power supply onto the two halves of the split-ring commutator.

As the motor rotates, the split ring commutator rotates with it. As the brushes remain stationary, this causes each side of the split ring commutator to be in contact with the positive brush for one half-turn, and the negative brush for the other half-turn. This causes the voltage polarity supplied from the brushes to the coil to flip every half-turn, also switching the current direction.

Because the brushes and split-ring commutator rely on a physical sliding contact to work, this is often the first part in a DC motor that needs to be replaced as the brushes are worn away.

To increase the power of a DC motor, there are three main approaches:

Increasing the strength of the magnetic field. This increases the $B$ term in the motor effect equation, creating a stronger force on the coil.
Adding more turns (loops) to the coil. This increases the total length of the coil, increasing the $L$ term in the motor effect equation and producing a stronger force.
Using a higher current in the coil. This increases the $I$ term in the motor effect equation, creating a stronger force.

The performance can also be improved by adding an iron core to the electromagnet rotor, as is shown in the more typical DC motor below.

Electric Motors Typical DC Motor Diagram StudySmarter Diagram of a typical DC motor, showing the rotor coil with many loops and an iron core to improve performance. Wikipedia.

A more advanced type of DC motor is the brushless motor. As the name suggests, the main difference in this type of motor is that it does not have the split-ring commutator or brush components. Instead, the DC supply voltage polarity is digitally varied using a semiconductor controller. This has the advantage of improved reliability, since the brushes often wear out in brushed motors and need to be replaced, and provides a better performance overall.

AC Motors

AC motors work using a similar principle to DC motors, but with several key differences. Generally, the coil windings form the stator (stationary part) of the motor, while the rotor is a permanent magnet or electromagnet.

In an AC power supply the voltage varies sinusoidally from positive to negative, as shown below. When an AC voltage is applied to the electromagnet stator coil windings, the varying voltage produces a varying magnetic field. In an AC motor, this varying magnetic field is used to produce a rotational force on the rotor and spin the motor. The split-ring commutator is no longer needed, since the current direction is reversed by the AC supply.

Electric Motors AC Voltage Graph StudySmarter (Top) - Sinusoidal variation of voltage in an AC power supply. (Bottom) - Corresponding magnetic field strength & direction produced by an electromagnet with an AC voltage applied. Ross MacDonald, StudySmarter Originals

Electric Motor Functions

Electric motors are found in countless devices we interact with every day. Household devices will generally use a DC motor if they are battery powered, and an AC motor if they are mains powered. This is to avoid having the convert the power supply from AC to DC or vice-versa, which would decrease efficiency and increase cost due to the extra components required. Below, you can see the applications of DC and AC motors in everyday use.

Household DC Motors:

Electric toothbrush
Laptop cooling fan
Remote-controlled car
Battery-powered drill
Vibration motor in a game controller
Car starter motor

Household AC Motors:

Extractor fan
Kitchen electric mixer
Vacuum cleaner
Washing machine
Microwave

Electric Motor Power Calculation

When calculating the power of an electric motor, there are two variables you should consider, the output power and the input power.

The output power of an electric motor

As power is equal to energy-per-second, we can calculate the output mechanical power of a motor by measuring the time taken to perform a known amount of work. A simple experiment design to do this could use a motor to lift a mass by winding it up on a string.

We know that work done is equal to a force multiplied by the distance its applied over:

$work done [J] = force [N] \times distance [m]$

The mechanical power of the motor (which is the output power of a motor) is found by dividing the amount of useful work done by the number of seconds it took to complete the work.

$P_{M e c h} [W] = P_{O u t} [W] = \frac{work done [J]}{time taken [s]}$

Input Power of an electric motor

The electric motor input power can be found using the general electric power equation. Note that this can be done because the input power of an electric motor is electrical power.

$P_{E l e c} = P_{I n} = Voltage [V] \times Current [A]$

Electric Motor Efficiency

The efficiency of a device is a way of measuring how much of the energy you put in is converted into useful output energy. A general formula for the efficiency of a device is:

$Efficiency = \frac{useful output power}{input power}$

For an electric motor, the input power is electrical and the output power is mechanical. The main source of waste energy in an electric motor is heat – this is produced both by the electrical resistance of the wire coils and friction between moving and static components.

The motor efficiency can be calculated by dividing the useful mechanical power output by the total electric power input. This is converted to a percentage efficiency by multiplying by 100.

${Efficiency}_{m o t o r} = \frac{P_{m e c h o u t}}{P_{e l e c i n}} \times 100 %$

Lifting a $20 N$ weight at a vertical distance of $1 m$ requires $20 J$ of work. A motor draws $0.75 A$ at $12 V$ for $3 s e c o n d s$ to lift the weight. Find:

The input power the motor used.
The output power of the motor.
The efficiency of the motor.

Input power

The input power of the motor is found by multiplying the voltage by the current drawn:

$P_{e l e c i n} = Voltage \times Current = 12 V \times 0.75 A = 9 W$

Output power

The output power of the motor is found by diving the amount of work performed by the time (in seconds) taken to do the work:

$P_{m e c h o u t} = \frac{work done}{time taken} = \frac{20 J}{3 s} = 6.67 W$

Motor efficiency

The motor’s efficiency is calculated by finding the proportion of input power that is converted to useful output power by the motor. To find efficiency as a percentage, we multiply the ratio by 100:

$E f f i c i e n c y_{m o t o r} = \frac{6.67 W}{9 W} \times 100 % = 74.1 %$

Electric Motors - Key takeaways

Electric motors work due to a phenomenon called the motor effect. The motor effect is the force generated on a current-carrying wire as it passes through a magnetic field.
The strength of the force can be increased by increasing either the magnetic field strength, current in the wire, or the length of wire in the magnetic field.
A DC motor uses a split-ring commutator to reverse the direction of the current in a wire coil every half-turn. This ensures the forces on the wire coil always continue to accelerate the coil's rotation and spin the motor.
An AC motor also uses the motor effect to spin but uses an AC power supply to vary the current direction instead of the split-ring commutator. Typically AC motors have the coil windings in the stator, and a permanent magnet or electromagnet rotor.
The efficiency of an electric motor can be calculated by measuring how much input energy is needed to perform a known amount of work.

Frequently Asked Questions about Electric Motor

How to calculate electric motor power?

Electric motor power can be calculated by measuring the time taken to do a known quantity of work. For example, lifting a 5N weight by 1m requires 5J of work. If the motor performs this work in 2 seconds, the output power can be calculated as 5J / 2S = 2.5W.

Alternatively, if the output shaft torque and rotation speed can be measured, mechanical power can also be calculated as:

Power = torque x rotational velocity,

where torque is measured in Nm and rotational velocity in radians per second.

What is the science behind electric motors?

Electric motors utilise the motor effect, which produces a force on a current carrying wire in a magnetic field. In a DC motor, a coil of wire is used so that each side experiences an opposite direction force in the magnetic field, causing the coil to rotate. Every half-turn, a split ring commutator flips the voltage polarity on the coil, reversing the current direction. Fleming’s left hand rule shows that this reverses the direction of the forces on the coil, ensuring it continues to be rotationally accelerated. Brushes are used to transfer the DC power supply to the rotating split-ring commutator.

What is electric motor and its efficiency?

The electric motor is an electro-mechanical device which converts input electric power to output mechanical power. To calculate efficiency, the proportion of input energy that is converted to useful output work must be calculated using the following equation:

Efficiency = (Useful output power) / (Input Power)

Which can also be represented as:

Efficiency = (Useful Mechanical Power) / (Electrical Power)

How does an electric motor work?

Why does an electric motor need a capacitor?

Certain types of single-phase AC motors can experience a problem of zero starting torque, due to the alternating magnetic field not producing a force in one direction for long enough to overcome the inertia. To overcome this, a secondary "starting coil" is sometimes included and is connected to the power supply through a starting capacitor, creating an LC circuit. As the AC current through a capacitor is 90 degrees ahead of the main phase, this initially provides power to the starting coil which gets the motor turning, before switching to the main coils once the motor is up to speed. Other motor designs use run capacitors to improve the power of the motor in operation.

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Electric Motor

StudySmarter Editorial Team