Transformer Fundamentals
A transformer transfers electrical energy between circuits via electromagnetic induction. The turns ratio determines how voltage and current are transformed — one goes up, the other comes down.
Core Equations
Turns Ratio: a = N₁/N₂ = V₁/V₂ = I₂/I₁
Secondary V: V₂ = V₁ × (N₂/N₁)
Secondary I: I₂ = I₁ × (N₁/N₂)
Power: P₁ = P₂ (ideal) → V₁I₁ = V₂I₂Worked Examples
Step-down, N1=2000, N2=100, V1=240V:
V₂ = 240 × (100/2000) = 12V
If I₂=5A: I₁ = 5 × (100/2000) = 0.25A
Step-up (grid), 11kV → 132kV:
a = 11/132 = 1:12 → N₂/N₁ = 12Real Transformer Efficiency
η = P_out / P_in = P_out / (P_out + P_losses)
Core losses: hysteresis + eddy current (constant)
Copper losses: I²R (increases with load)
Distribution transformer: η ≈ 97-99%VA Rating
- VA = V × I (apparent power)
- Select transformer VA ≥ 125% of continuous load
- Common sizes: 25 VA (door bell) to 1000 kVA (substation)
Calculate transformer ratios: Free Transformer Calculator
Transformer Fundamentals
- Turns ratio: N₁/N₂ = V₁/V₂ = I₂/I₁
- Voltage transformation: V₂ = V₁ × (N₂/N₁)
- Current transformation: I₂ = I₁ × (N₁/N₂)
- Power conservation: V₁I₁ ≈ V₂I₂ (ignoring losses, typically 1–3%)
- Impedance transformation: Z_reflected = Z_load × (N₁/N₂)²
Transformer Ratings and Applications
Transformers are rated in kVA (apparent power), not kW, because they are limited by winding current (which causes I²R heating) regardless of load power factor. A 100 kVA transformer can supply 100 kW at unity PF or 80 kW at PF 0.8 — the apparent power (current drawn) is the same. Transformer efficiency is typically 98–99% at full load but drops significantly at low loads. Distribution transformers step down from 11 kV or 33 kV to 400 V for building supply. Isolation transformers are used for safety (no earth continuity) and reducing interference. Auto-transformers use a single winding tapped at intermediate points — compact and efficient but without galvanic isolation.
Frequently Asked Questions
Why can transformers not work on DC?
Transformers work by electromagnetic induction — a changing magnetic flux in the core induces voltage in the secondary winding. DC creates a constant (non-changing) flux, which induces no voltage. At DC, the primary winding acts as a short circuit (pure resistance), drawing very high current and causing overheating. Transformers are fundamentally AC devices; DC-DC conversion requires switching electronics (switch-mode power supplies).
What causes transformer hum?
Magnetostriction — the core material physically changes dimension as it magnetises and demagnetises 50/60 times per second (at fundamental frequency). The resulting vibration at 100/120 Hz (twice supply frequency) produces the characteristic hum. Higher harmonics in the supply (from non-linear loads) create higher frequency noise components. Mounting transformers on anti-vibration pads reduces structure-borne noise transmission.
What is transformer vector group (e.g., Dyn11)?
Vector group describes the winding configuration (Delta D or Star Y on each side) and the phase shift between primary and secondary. Dyn11 means: primary Delta (D), secondary star with neutral (yn), 11 o'clock phase shift (330° or -30°). The phase shift matters when paralleling transformers — they must have the same vector group to avoid circulating currents. Most UK distribution transformers are Dyn11.