Transformers

A transformer is one of the most important electrical devices ever invented — quietly responsible for making modern power grids possible. Every time electricity travels from a power station to your home, it passes through multiple transformers that change its voltage, sometimes by factors of hundreds. At its heart, a transformer is an application of Faraday's law of electromagnetic induction: a changing magnetic flux in one coil of wire induces an EMF in a nearby coil, allowing energy to be transferred between circuits that are not physically connected. Transformers work exclusively with alternating current (AC). Because AC continuously changes direction, it creates a continuously changing magnetic field, which in turn creates a continuously changing flux through a second coil — inducing an alternating voltage in that coil. Direct current (DC), by contrast, would produce a static magnetic field, zero change in flux, and therefore zero induced EMF. This is precisely why the world's power grid uses AC rather than DC: transformers make AC voltage easy to step up or step down, enabling efficient long-distance transmission. A step-up transformer increases voltage (and correspondingly decreases current), while a step-down transformer decreases voltage (and increases current). The ratio between output and input voltage is governed by the turns ratio — the ratio of the number of wire loops in each coil. Because energy must be conserved, whatever you gain in voltage you lose in current. Real transformers are remarkably efficient, often exceeding 98%, making them essential components in power distribution, consumer electronics chargers, and industrial equipment.

Key takeaways
  • The Iron Core and Mutual Inductance
  • Faraday's Law in Each Coil
  • Step-Up vs. Step-Down
  • Current and Energy Conservation

The Iron Core and Mutual Inductance

A transformer consists of two coils — the primary coil (connected to the input voltage source) and the secondary coil (connected to the load) — wound around a shared iron core. The iron core is laminated (made of thin insulated sheets) to reduce energy losses from eddy currents. When AC flows through the primary coil, it creates a constantly changing magnetic field. Because both coils share the same iron core, nearly all of the magnetic flux produced by the primary coil passes through the secondary coil as well. This sharing of flux is called mutual inductance.

Faraday's Law in Each Coil

By Faraday's law, the EMF induced in any coil equals the number of turns multiplied by the rate of change of magnetic flux: ε = −N(dΦ/dt). Both the primary and secondary coils experience the same rate of change of flux (dΦ/dt) because they share the same core. Therefore the voltage across each coil is simply proportional to its number of turns. If the primary has N₁ turns and the secondary has N₂ turns, then V₂/V₁ = N₂/N₁. This is the transformer equation.

Step-Up vs. Step-Down

If N₂ > N₁, the secondary voltage is higher than the primary voltage — this is a step-up transformer. Power stations use step-up transformers to raise voltages to hundreds of thousands of volts for long-distance transmission, dramatically reducing resistive power losses (since P_loss = I²R, and less current means less loss). If N₂ < N₁, it is a step-down transformer. The transformer near your home steps voltage down from thousands of volts to the 120 V or 230 V used in household outlets. The phone charger on your desk contains a further step-down transformer to produce the 5 V your device needs.

Current and Energy Conservation

An ideal transformer conserves power: P_in = P_out, meaning V₁I₁ = V₂I₂. If the secondary voltage is doubled, the secondary current is halved. Think of it like a hydraulic lever: you can trade force for distance (or voltage for current) but you cannot create energy from nothing. In reality, small losses occur due to resistance in the coils (copper losses), eddy currents in the core (despite lamination), and hysteresis — the energy needed to repeatedly magnetise and demagnetise the iron core. Modern power transformers account for all these effects and still achieve efficiencies above 98%.

The Key Equation

VsVp=NsNpandVpIp=VsIs\frac{V_s}{V_p} = \frac{N_s}{N_p} \quad \text{and} \quad V_p I_p = V_s I_s
  • V_p — Primary voltage (V): The AC voltage applied to the input (primary) coil.
  • V_s — Secondary voltage (V): The AC voltage produced at the output (secondary) coil.
  • N_p — Primary turns (dimensionless): Number of loops of wire in the primary coil.
  • N_s — Secondary turns (dimensionless): Number of loops of wire in the secondary coil.
  • I_p — Primary current (A): Current flowing in the primary coil.
  • I_s — Secondary current (A): Current delivered by the secondary coil to the load.

Worked Example

Problem. A step-down transformer has 2400 turns on the primary coil and 120 turns on the secondary coil. The primary voltage is 240 V AC. (a) What is the secondary voltage? (b) If the secondary coil delivers a current of 10 A to a load, what is the primary current? Assume the transformer is ideal.

Vs=12 V,Ip=0.5 AV_s = 12\,\text{V}, \quad I_p = 0.5\,\text{A}

Answer. Secondary voltage = 12 V; Primary current = 0.5 A

Figure
Diagram
IronCoreACLoadPrimaryN_p turnsV_p, I_pSecondaryN_s turnsV_s, I_sTransformer — Mutual InductionChanging flux Φ links both coils through iron core
Origins · 1 minNikola Tesla and how this was discovered
NT
Nikola Tesla
1856–1943 · Serbian-American

Tesla championed alternating current (AC) power systems over Thomas Edison's direct current (DC) systems in the famous 'War of Currents' of the 1880s–90s. He developed the AC induction motor and worked closely with George Westinghouse to demonstrate that AC, combined with transformers for efficient voltage conversion, could deliver electricity across vast distances cheaply and safely — the system that powers the world today. Tesla could reportedly perform integral calculus in his head and often visualized and mentally tested his inventions completely before ever building a physical prototype, claiming he could detect flaws in a design through imagination alone.

  • Faraday's Law of Induction — Transformer operation is a direct application of Faraday's law — the induced EMF in each coil equals N(dΦ/dt), which gives the turns-ratio voltage relationship.
  • Mutual Inductance — Mutual inductance quantifies how effectively a changing current in one coil induces an EMF in another — the physical mechanism inside every transformer.
  • AC Power and RMS Values — Transformer voltage and current ratings are given as RMS values; understanding AC power is essential to calculating transformer efficiency and load behaviour.
  • Eddy Currents — Eddy currents are a key energy-loss mechanism in transformer cores, which is why cores are laminated — directly relevant to real transformer design.