Transformer Core Cutaway

Flux. Faraday's law for a sinusoidal supply gives the peak flux density B = V1 / (4.44 f N1 A). Raising voltage or lowering frequency raises B; above the knee the steel saturates and the magnetising current spikes.

Core loss. Hysteresis (Steinmetz): Ph = kh f Bn Vcore. Classical eddy loss of a sheet of thickness t: Pe = (π2 σ f2 B2 t2 / 6) Vcore, so halving the sheet thickness cuts eddy loss by 4. For thick sheets the field cannot penetrate: the model multiplies by the exact slab factor 3/x (sinh x - sin x)/(cosh x - cos x), x = t/δ, with skin depth δ = 1/√(π f μ σ).

Equivalent circuit. Series R₁+R₂' = 0.32 Ω, X₁+X₂' = 0.80 Ω (2 % and 5 % of the 16 Ω base) with the core branch (loss current in phase, magnetising current from the B-H curve) shunted at the primary terminals. Voltage regulation ≈ R_pu cosφ ± X_pu sinφ. Efficiency peaks when copper loss equals core loss, at x = √(P₀/P_sc) of rated load.

Tests. Open circuit at rated voltage gives core loss P₀, R_c and X_m; short circuit at rated current gives P_sc, R_eq and X_eq. Efficiency predicted from test data alone is compared with the full circuit solution above.

Simplifications, stated honestly. Single phase, linear leakage, no excess (anomalous) loss, no hysteresis loop in the magnetising current (anhysteretic H(B)), fixed relative permeability for the skin depth, magnetising-current fundamental used in the phasor solution (the distortion is shown as THD), lumped thermal model with illustrative constants. Material constants are typical order-of-magnitude values for each class, not a datasheet; the 10 kVA unit is a made-up round-number design. The 3D picture shows 36 plates for clarity; a real core has hundreds.

Independent educational model. Flux sparks are a visual aid at 1/100 speed.