Advanced · 14 min
Induction and ideal transformers
Relate changing magnetic flux to induced voltage and calculate transformer ratios.
Changing flux induces voltage
Magnetic flux describes the magnetic field passing through an area. For a uniform field perpendicular to a flat area, flux is Φ = B × A, measured in webers (Wb). The average induced electromotive force magnitude in a coil is |ε| = N × |ΔΦ| ÷ Δt when the same flux passes through each turn. Despite its name, electromotive force is a voltage, measured in volts. Lenz's law gives a direction that opposes the change in flux.
Worked example
A 100-turn coil's flux per turn changes by 0.002 Wb in 0.05 s. Average induced voltage magnitude = 100 × 0.002 ÷ 0.05 = 4 V
Transformers transfer energy
An ideal transformer uses a changing magnetic flux linking two coils. For alternating voltage, the voltage ratio equals the turns ratio: Vs/Vp = Ns/Np. A smaller secondary turn count reduces voltage. Ideal input and output powers are equal, so a lower output voltage can accompany a higher output current under load. Real transformers lose energy. A steady direct current does not provide the sustained changing flux needed for ordinary transformer operation; use diagrams or simulations for these exercises.
Worked example
An ideal transformer has 400 primary turns and 100 secondary turns. With 24 V alternating input, output voltage = 24 × 100 ÷ 400 = 6 V.
Model induction on paper
- For the same coil and flux change, predict what happens to average induced voltage if the change takes half as long.
- Draw an ideal transformer with 200 primary turns and 100 secondary turns. For 12 V alternating input, calculate its output voltage.