Transformers and Loudspeakers

Two more devices complete the story of P4, and both bring the topic full circle. The loudspeaker uses the motor effect to turn an electrical signal back into sound — the exact reverse of the microphone from the last lesson. The transformer uses electromagnetic induction to change the size of an alternating voltage, and it is the device that makes the National Grid possible: it steps voltages up to huge values for efficient transmission and back down to safe values for our homes. This lesson, part of Topic P4 (Magnetism and magnetic fields) of OCR Gateway Science A, explains the moving-coil loudspeaker, how a transformer works, the Higher-tier transformer equations, and why high voltages reduce energy losses in power lines.

By the end of this lesson you should be able to explain how a moving-coil loudspeaker works using the motor effect, describe the structure and action of step-up and step-down transformers, use the Higher-tier transformer equations, and explain why the National Grid transmits power at high voltage.

The Moving-Coil Loudspeaker

A moving-coil loudspeaker turns an electrical signal into sound using the motor effect — it is the mirror-image of the microphone, which used the generator effect. Inside the loudspeaker, a coil is attached to a paper cone (the diaphragm) and sits in the field of a permanent magnet.

When an alternating current from the amplifier flows through the coil, the coil sits in the magnetic field and so feels a force by the motor effect. Because the current is constantly varying (it carries the audio signal), the force on the coil constantly varies too — pushing the coil (and the cone) back and forth. The vibrating cone pushes on the air, creating pressure variations that travel out as a sound wave. The frequency of the alternating current sets the frequency (pitch) of the sound, and a bigger current gives a bigger force, a larger vibration, and so a louder sound.

Headphones work in exactly the same way — they are simply two tiny loudspeakers, one for each ear.

graph LR
  A[Varying a.c. signal] --> B[Coil in magnetic field]
  B --> C[Varying force - motor effect]
  C --> D[Cone vibrates back and forth]
  D --> E[Sound wave produced]

Exam Tip: A loudspeaker uses the motor effect: a varying current in a coil produces a varying force that vibrates a cone to make sound. It is the opposite of the microphone (generator effect). Don't mix the two up — match the device to the effect.

What a Transformer Does

A transformer changes the size of an alternating potential difference (voltage). It has two coils of insulated wire wound onto a soft-iron core:

the primary coil, connected to the input a.c. supply;
the secondary coil, connected to the output.

The two coils are not electrically connected to each other — the only link between them is the soft-iron core. Here is how it works, step by step:

The alternating current in the primary coil produces a constantly changing magnetic field.
The soft-iron core carries (concentrates) this changing magnetic field round to the secondary coil.
The changing magnetic field through the secondary coil induces an alternating potential difference across it (the generator effect).

Because the whole process depends on a changing magnetic field, a transformer only works with alternating current. If you connected a d.c. supply, the magnetic field would be steady (not changing), nothing would be induced in the secondary, and the output would be zero. This is one of the main reasons mains electricity is a.c.

The number of turns on each coil decides whether the voltage goes up or down:

a step-up transformer has more turns on the secondary than the primary, and increases the voltage;
a step-down transformer has fewer turns on the secondary than the primary, and decreases the voltage.

Exam Tip: A transformer works only on a.c. because it needs a changing magnetic field to induce a voltage in the secondary. More turns on the secondary → step-up (voltage up); fewer turns on the secondary → step-down (voltage down). The coils are linked only by the soft-iron core.

The Transformer Equation (Higher tier)

(Higher tier) The output voltage of a transformer depends on the ratio of the number of turns on the two coils. The potential differences are in the same ratio as the numbers of turns:

$\dfrac{V_p}{V_s} = \dfrac{N_p}{N_s}$

where

$V_p$ and $V_s$ are the primary and secondary potential differences (in volts, $\text{V}$ );
$N_p$ and $N_s$ are the numbers of turns on the primary and secondary coils.

Worked Example 1 — A step-up transformer

A transformer has $100$ turns on its primary coil and $500$ turns on its secondary coil. The primary is connected to a $230 \text{ V}$ a.c. supply. Calculate the output (secondary) voltage. (Higher)

Step 1 — write the equation: $\dfrac{V_p}{V_s} = \dfrac{N_p}{N_s}$ .

Step 2 — rearrange to make $V_s$ the subject: $V_s = V_p \times \dfrac{N_s}{N_p}$ .

Step 3 — substitute: $V_s = 230 \times \dfrac{500}{100}$ .

Step 4 — calculate: $V_s = 230 \times 5 = 1150 \text{ V}$ .

Answer: the output is $1150 \text{ V}$ . Since the secondary has more turns, this is a step-up transformer.

Worked Example 2 — A step-down transformer

A transformer steps a $230 \text{ V}$ supply down to $11.5 \text{ V}$ . The primary has $4000$ turns. Calculate the number of turns on the secondary. (Higher)

Step 1 — write the equation: $\dfrac{V_p}{V_s} = \dfrac{N_p}{N_s}$ .

Step 2 — rearrange to make $N_s$ the subject: $N_s = N_p \times \dfrac{V_s}{V_p}$ .

Step 3 — substitute: $N_s = 4000 \times \dfrac{11.5}{230}$ .

Step 4 — calculate: $N_s = 4000 \times 0.05 = 200$ turns.

Answer: the secondary has $200$ turns. Fewer turns than the primary confirms it is a step-down transformer.

Exam Tip: (Higher) In $\dfrac{V_p}{V_s} = \dfrac{N_p}{N_s}$ , keep the primary quantities together on the top and the secondary together on the bottom. A quick check: if the voltage went up, the secondary must have more turns (and vice versa).

The Ideal Transformer and Power (Higher tier)

(Higher tier) A transformer cannot create energy. In an ideal transformer — one that is 100% efficient — the power put into the primary equals the power taken from the secondary. Since power is $P = VI$ , this gives:

$V_p I_p = V_s I_s$

where $I_p$ and $I_s$ are the currents (in amperes) in the primary and secondary coils. An important consequence follows: if a transformer steps the voltage up, it must step the current down by the same factor (and vice versa), so that the product $VI$ — the power — stays the same.

Worked Example 3 — Finding the secondary current

An ideal step-up transformer raises $230 \text{ V}$ to $11\,500 \text{ V}$ . The current in the primary is $8.0 \text{ A}$ . Calculate the current in the secondary. (Higher)

Step 1 — write the power equation for an ideal transformer: $V_p I_p = V_s I_s$ .

Step 2 — rearrange to make $I_s$ the subject: $I_s = \dfrac{V_p I_p}{V_s}$ .

Step 3 — substitute: $I_s = \dfrac{230 \times 8.0}{11\,500}$ .

Step 4 — calculate: $I_s = \dfrac{1840}{11\,500} = 0.16 \text{ A}$ .

Transformers and Loudspeakers (Higher)