2022 A/L Physics Past Paper · Question 05 (English Medium)

When the back e.m.f. of a motor is greatest

The back e.m.f. in an electric motor is maximum when the motor

Answer and explanation

Answer: (4) is at its maximum speed.

What the question asks

We want: the moment when the back e.m.f. of a motor is greatest.

What each letter means:

$E$ ( $\text{V}$ ): back e.m.f.

$V$ ( $\text{V}$ ): supply voltage.

$R_a$ ( $\Omega$ ): resistance of the armature.

$I_a$ ( $\text{A}$ ): current in the armature.

$B$ ( $\text{T}$ ): flux density of the magnetic field.

$\omega$ ( $\text{rad s}^{-1}$ ): speed of rotation of the armature.

This back emf is proportional to the flux density of the magnetic field and the speed of rotation of the armature.

When the motor is activated its back e.m.f. is zero but the current develops fast along with the speed of the armature.

For example, think of a bicycle dynamo that lights a lamp.

When you pedal slowly, the lamp glows dimly. The dynamo gives only a small voltage.

When you pedal faster, the lamp glows brighter. The dynamo gives a bigger voltage.

A motor does the same job while it turns. Its coil turns in a magnetic field, so it also acts as a dynamo.

$E \propto B\,\omega$

In words: the back e.m.f. is bigger when the field is stronger and when the armature turns faster.

So $E$ is greatest when $\omega$ is greatest. That is when the motor is at its maximum speed.

The book says the same.

The back e.m.f. is proportional to the speed of rotation of the armature.

At the moment of starting the speed is zero, so the back e.m.f. is zero.

As the speed grows, the back e.m.f. grows.

It is greatest when the speed is greatest.

A motor that is not operating is not turning, so its back e.m.f. is zero.

At the moment of starting the back e.m.f. is zero.

While the speed is increasing, the back e.m.f. is still growing. It has not reached its greatest value.

While the speed is decreasing, the back e.m.f. is falling.

The back e.m.f. is proportional to the speed of rotation of the armature.

So it is greatest when the motor is at its maximum speed.

The answer is (4).

Back e.m.f. goes up and down with the speed of the motor.

Zero speed, zero back e.m.f. Greatest speed, greatest back e.m.f.

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