2D Transformer Simulator — Mutual Induction & Efficiency

Preset

Coils

Primary turns N₁ 100

Secondary turns N₂ 400

Source & Load

V₁ peak 120 V

Load resistance 100 Ω

Frequency 50 Hz

Model

Ideal coupling — no losses, 100% efficiency.

Live Readout

Turns ratio N₂/N₁

4.00

V₂ peak

480 V

I₂ peak

4.80 A

I₁ peak

19.20 A

P₁ in

1152 W

P₂ out

1152 W

Efficiency

100.0%

Losses (core+Cu)

0 W

How it works

An AC source drives the primary coil (N₁ turns), setting up a shared, time-varying magnetic flux Φ(t) in the core. By Faraday's law the induced EMF in each winding is proportional to its own turn count and to dΦ/dt: ε₁ = −N₁·dΦ/dt and ε₂ = −N₂·dΦ/dt. Because both windings link the same flux, their EMFs are always in the fixed ratio ε₂/ε₁ = N₂/N₁ — this is genuine mutual-inductance coupling, not a hardcoded scale factor. Integrating ε₁ = −N₁·dΦ/dt shows the flux itself lags the driving voltage by 90°, exactly as in a real transformer core.

With a resistive load R₨ on the secondary, the simulator solves the loop equations for the induced secondary current I₂ = V₂/R₨ and reflects it back to the primary through the turns ratio, so power is conserved at the ideal limit: V₁·I₁ = V₂·I₂. Switch on "real transformer" to add copper loss (I²R heating in each winding, scaled by the wire length each turn count implies) and core loss (a magnetizing-branch resistance that worsens with frequency, modeling hysteresis and eddy currents). Both losses reduce the output below the ideal prediction and pull efficiency below 100%, matching how real power and distribution transformers actually behave.