Electromagnetic Induction and Transformers
Electromagnetic Induction
When a conductor moves through a magnetic field — or when a magnetic field changes around a stationary conductor — a electromagnetic induction occurs. The result is an induced electromotive force (EMF). If the conductor forms part of a closed circuit, this EMF drives a current. If the circuit is open, only a voltage appears across the ends of the conductor.
Three factors control how large the induced EMF is. Moving the conductor faster increases the rate at which field lines are cut, so the induced EMF rises. Using a stronger magnet increases the field strength, again boosting the EMF. Adding more turns to a coil multiplies the effect because each turn contributes its own induced EMF. Reversing the direction of motion — or reversing the magnet — reverses the direction of the induced current.
Increasing the speed of motion, the magnetic field strength, or the number of coil turns all increase the induced EMF. Reversing the motion reverses the current direction.
The Generator Effect
The generator effect is used in every electrical generator. In an alternator, a coil rotates continuously inside a magnetic field. As the coil spins, the angle between the coil and the field lines changes constantly, so the rate of cutting field lines changes too. This produces an alternating voltage — one that regularly reverses direction — which is the basis of the alternating current (AC) supplied to homes and businesses.
A dynamo uses a similar rotating coil but includes a split-ring commutator. This device swaps the connections to the external circuit every half-turn, so the output voltage always points the same way. The result is a pulsating direct current (DC) rather than a smooth AC output.
Microphones and Loudspeakers
A dynamic microphone converts sound into an electrical signal using the generator effect. A thin diaphragm is attached to a coil of wire sitting inside a permanent magnet. When sound waves reach the microphone, the diaphragm vibrates, moving the coil back and forth in the magnetic field. This motion induces a varying EMF that mirrors the pattern of the sound wave.
A loudspeaker works in reverse: an alternating current through a coil in a magnetic field creates a varying force (by the motor effect), which vibrates the cone and produces sound. The pair — microphone and loudspeaker — demonstrates how electrical and mechanical energy convert back and forth via electromagnetic principles.
Transformers
A transformer changes the voltage of an AC supply. It consists of a primary coil and a secondary coil, both wound around a shared iron core. When alternating current flows in the primary coil, it creates a constantly changing magnetic field in the iron core. This changing field passes through the secondary coil and induces an alternating EMF in it — the process of mutual induction.
The iron core is chosen because it is easily magnetised and demagnetised many times per second, allowing it to carry the changing magnetic field efficiently between the coils. The coils are electrically insulated from each other and from the core, so there is no direct electrical connection — energy is transferred entirely by the changing magnetic field.
The turns-ratio equation links the voltages and numbers of turns in a transformer:
$$\frac{V_p}{V_s} = \frac{N_p}{N_s}$$
where \(V_p\) is the primary voltage, \(V_s\) is the secondary voltage, \(N_p\) is the number of primary turns, and \(N_s\) is the number of secondary turns.
Step-Up and Step-Down Transformers
A step-up transformer has more turns on the secondary coil than the primary coil (\(N_s > N_p\)), so the output voltage is higher than the input. A step-down transformer has fewer turns on the secondary (\(N_s < N_p\)), so it reduces the voltage. The ratio of turns equals the ratio of voltages.
Question: A transformer has 500 turns on its primary coil and 50 turns on its secondary. The primary voltage is 230 V. Calculate the secondary voltage.
Step 1 — Write the equation:
$$\frac{V_p}{V_s} = \frac{N_p}{N_s}$$
Step 2 — Substitute:
$$\frac{230}{V_s} = \frac{500}{50}$$
Step 3 — Rearrange and solve:
$$V_s = \frac{230 \times 50}{500} = 23 \text{ V}$$
This is a step-down transformer — 10 times fewer secondary turns means 10 times lower output voltage.
Power and Efficiency in Transformers
For a transformer assumed to be 100% efficient (no energy losses), the power delivered to the primary coil equals the power output from the secondary coil. Since power equals voltage multiplied by current, this gives the power equation:
$$V_p I_p = V_s I_s$$
This equation reveals an important consequence: when a step-up transformer increases voltage, the current must decrease by the same factor. If voltage doubles, current halves. This trade-off is why high-voltage transmission saves energy, as explored in the next section.
Question: A step-up transformer has 400 turns on the primary and 8,000 turns on the secondary. The primary voltage is 25 V and the primary current is 4.0 A. Assuming 100% efficiency, calculate (a) the secondary voltage and (b) the secondary current.
Part (a) — Secondary voltage using turns-ratio:
$$\frac{25}{V_s} = \frac{400}{8000} \Rightarrow V_s = \frac{25 \times 8000}{400} = 500 \text{ V}$$
Part (b) — Secondary current using power equation:
$$V_p I_p = V_s I_s \Rightarrow 25 \times 4.0 = 500 \times I_s$$
$$I_s = \frac{100}{500} = 0.20 \text{ A}$$
The current fell from 4.0 A to 0.20 A — a factor of 20, matching the voltage increase.
The National Grid and Transmission Losses
Electricity generated at a power station is transmitted across the country through the National Grid — a network of cables connecting power stations to homes, schools, and businesses. Cables have electrical resistance, and whenever current flows through a resistor, energy is lost as heat. The power lost in a cable is given by:
$$P_{\text{loss}} = I^2 R$$
Because power loss depends on the square of the current, even a modest reduction in current produces a dramatic reduction in energy wasted. Doubling the voltage halves the current, which reduces the cable losses to one quarter. This is why the National Grid transmits electricity at very high voltages — typically hundreds of thousands of volts — for long-distance transmission.
At the power station, a step-up transformer raises the generated voltage to this high transmission voltage. Near consumers, step-down transformers progressively reduce the voltage to the safe levels used in homes (230 V) and industry. The whole system depends on the fact that transformers only work with alternating current.
Real transformers are not perfectly efficient. Energy is lost as heat in the resistance of the coils and through eddy currents induced in the iron core. Modern transformer designs — using laminated cores to reduce eddy currents — achieve efficiencies above 99%, making the losses very small in practice.