Physics · Lesson 23

Electromagnetic induction, transformers & a.c. circuits

JAMBWAECNECO

What the syllabus asks

JAMB: Electromagnetic induction, Faraday’s and Lenz’s laws, generators, transformers, inductance, eddy currents; simple a.c. circuits: peak and r.m.s. values, reactance, impedance, resonance, power factor

WAEC: Electromagnetic induction: Faraday’s and Lenz’s laws, induced e.m.f., a.c. and d.c. generators, transformers (turns ratio, efficiency, energy losses), power transmission, self and mutual induction, eddy currents, induction coil; alternating current: peak and r.m.s. values, reactance, impedance, series R–L–C circuits, resonance, power in a.c. circuits

NECO: Electromagnetic induction: Faraday’s and Lenz’s laws, induced e.m.f., a.c. and d.c. generators, transformers (turns ratio, efficiency, energy losses), power transmission, self and mutual induction, eddy currents, induction coil; alternating current: peak and r.m.s. values, reactance, impedance, series R–L–C circuits, resonance, power in a.c. circuits

What you will learn

Describe experiments showing electromagnetic induction and state Faraday’s and Lenz’s laws.
Calculate induced e.m.f. from E = NΔΦ/Δt and E = BLv, and find its direction.
Explain the a.c. and d.c. generators and the factors that affect their output.
Explain the transformer, use the turns-ratio and efficiency equations, and describe how losses are reduced.
Explain why power is transmitted at high voltage and calculate cable losses.
Distinguish peak and r.m.s. values and calculate reactance and impedance.
Analyse series R–L–C circuits, including resonance and power factor.

Key points

Changing flux induces an e.m.f.: E = NΔΦ/Δt; moving wire E = BLv.
Lenz: induced current opposes the change (energy conservation).
Fleming’s right-hand rule gives the induced current direction.
a.c. generator uses slip rings; d.c. generator uses a commutator; E₀ = NBAω.
Transformer: Vₛ/Vₚ = Nₛ/Nₚ; ideal VₚIₚ = VₛIₛ; works only on a.c.
Losses: copper, eddy currents (laminate), hysteresis (soft iron), flux leakage.
Transmit at high voltage to cut I²R loss.
Self-inductance: E = L ΔI/Δt; energy ½LI².
V_rms = V₀/√2; Nigerian mains about 230 V r.m.s., 50 Hz.
X_L = 2πfL, X_C = 1/(2πfC), Z = √(R² + (X_L − X_C)²); resonance f₀ = 1/(2π√LC).

Start here: Discovering induction

In the lesson “Magnetism & electromagnetism” you saw that an electric current produces a magnetic field. In 1831 Michael Faraday asked the reverse question: can magnetism produce electricity? The answer is yes, but only when something is changing. Every generator at Kainji and Shiroro hydroelectric dams, every generator set (“gen”) humming outside a shop, depends on this discovery.

The simple experiment: connect a coil of wire to a sensitive galvanometer. Push a bar magnet into the coil: the needle flicks one way. Hold the magnet still inside the coil: the needle returns to zero. Pull the magnet out: the needle flicks the other way. Move the coil instead of the magnet: the same thing happens.

Electromagnetic induction: an e.m.f. is induced in a conductor whenever the magnetic flux linking it changes. If the circuit is complete, an induced current flows.

The deflection is larger when: (1) the magnet moves faster, (2) the magnet is stronger, (3) the coil has more turns. A coil with an iron core increases it further.

The key quantity is magnetic flux Φ = BA, the “amount of field” passing through an area, measured in webers (Wb). A coil of N turns has flux linkage NΦ.

⚠️ Common mistake: thinking a strong magnet sitting still inside a coil produces current. No change, no induced e.m.f.

Try it yourself. State three ways to increase the deflection of the galvanometer.

Show solution

Move the magnet faster, use a stronger magnet, use more turns (or insert a soft-iron core).

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Practice questions

1. A 300-turn coil has its flux change by 0.02 Wb in 0.1 s. Find the e.m.f.

Show worked answer

300 × 0.02/0.1 = 60 V.

2. A 0.5 m wire moves at 4 m/s perpendicular to a 0.3 T field. Find the e.m.f.

Show worked answer

0.3 × 0.5 × 4 = 0.6 V.

3. A transformer steps 240 V down to 6 V. The primary has 2000 turns. Find the secondary turns.

Show worked answer

2000 × 6/240 = 50 turns.

4. A transformer is 80% efficient. It delivers 48 W. Find the input power.

Show worked answer

48/0.8 = 60 W.

5. State two ways of reducing energy losses in a transformer.

Show worked answer

Any two: laminated core, soft-iron core, thick copper windings, good core design.

Key words

Magnetic flux (Φ): The product of flux density and the area it passes through at right angles, Φ = BA; unit weber (Wb).
Electromagnetic induction: The production of an e.m.f. in a conductor when the magnetic flux linking it changes.
Faraday’s law: The induced e.m.f. is proportional to the rate of change of flux linkage.
Lenz’s law: The induced current flows in a direction that opposes the change producing it.
Fleming’s right-hand rule: Thumb = motion, first finger = field, second finger = induced current (generators).
Slip rings: Rings that keep each end of a generator coil connected to the same brush, giving a.c.
Commutator: A split ring that reverses connections every half-turn, giving d.c.
Transformer: A device that changes an alternating voltage using mutual induction.
Eddy currents: Circulating currents induced in a solid metal core; they waste energy as heat.
Self-induction: An e.m.f. induced in a coil by a change in its own current.
Mutual induction: An e.m.f. induced in one coil by a changing current in a nearby coil.
r.m.s. value: The steady d.c. value that would give the same heating effect; V₀/√2 for a sine wave.

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