Transformer Playground

Animated two-winding ideal transformer. Sliders for primary turns N₁, secondary turns N₂, primary voltage V₁, and rated load power P. Watch the core flux Φ (red arrows) pulse with V₁/N₁, the winding-current halos track |I sin ωt|, and every output number trace back to V₂ = V₁ · (N₂/N₁), I₂ = P / V₂, I₁ = I₂ · (N₂/N₁) in the derivation card.

Number of red arrows = peak flux amplitude (set by V₁ / N₁; independent of N₂ and load). They reverse every half-cycle. Blue / orange halos around each winding grow with the instantaneous primary / secondary current. Load is constant-power: pick P, and I₂ adjusts to satisfy P = V₂·I₂ — so halving V₂ doubles I₂.

Primary turns N₁1000

Secondary turns N₂100

Primary voltage V₁ (V_rms)230 V

Load power P (W)10.0 W

Primary V₁

230.00 V

Primary I₁

43.48 mA

Secondary V₂

23.00 V

Secondary I₂

434.78 mA

How V₂, I₂, I₁ are calculated

V₂ = V₁ · (N₂ / N₁)=230 · (100/1000)=23.00 V

I₂ = P / V₂=10 / 23.00=434.78 mA

I₁ = I₂ · (N₂ / N₁)=0.435 A · (100/1000)=43.48 mA

Same flux per turn forces the voltage ratio V₂/V₁ = N₂/N₁. A constant-power load pins I₂ at P/V₂. MMF balance (N₁I₁ = N₂I₂) then inverts the turn ratio for the currents — that's why a step-down transformer pulls a small primary current and delivers a large secondary current.

Operating point (ideal transformer, constant-power load)

Turns ratio n = N₁/N₂10.00Output power P_out10.00 WPrimary power P_in10.00 WLoad as equivalent R52.9 Ω

Quick experiments

Step-down vs step-up. Keep V₁ = 230 V. N₁ = 1000, N₂ = 100 gives a 10:1 step-down (V₂ ≈ 23 V). Swap them — 10:1 step-up (V₂ ≈ 2.3 kV). Same box.
V₂ halves → I₂ doubles. Keep P fixed at 10 W and double N₁. V₂ halves, I₂ doubles — the textbook constant-power rule made visible.
Flux follows V/N. Raise V₁ (more red arrows). Raise N₁ (fewer red arrows). Change N₂ or P — flux unchanged; only the currents respond.
MMF balance N₁ I₁ ≈ N₂ I₂. Multiply the live V₁·I₁ and V₂·I₂ — they match P. This is power conservation, and it's also why the blue and orange halos change together as you move P.

Transformer fundamentals

A transformer transfers AC power between two electrically isolated circuits via a shared magnetic core. The turns ratio n = N₁/N₂ sets the voltage and current scaling; an ideal transformer conserves power (V₁ × I₁ = V₂ × I₂).

Voltage, current, and impedance scaling

Voltage: V₂ = V₁ / n (step-down if n > 1)
Current: I₂ = I₁ × n (current rises as voltage falls)
Impedance: Z_in = n² × Z_load — used for impedance matching to maximise power transfer

Real-world losses

Practical transformers lose power to copper losses (I²R in the windings), core losses (hysteresis and eddy currents in the iron core), and leakage flux (flux that doesn't link both windings). Efficiency of a well-designed 50/60 Hz transformer is typically 95–99 %.

Learn more → Transformers — Learn

Formula reference

Turns ratio: $n = \dfrac{N_p}{N_s} = \dfrac{V_p}{V_s}$
A 10:1 transformer takes 240 V to 24 V.
Current transforms inversely: $\dfrac{I_s}{I_p} = \dfrac{N_p}{N_s}$
Step voltage down and current steps up by the same factor.
Impedance transforms with the square: $Z_p = n^{2} Z_s$
A 10:1 ratio makes an 8 Ω speaker look like 800 Ω.
Efficiency: $\eta = \dfrac{P_{out}}{P_{in}}$
Real transformers reach 95–99 %; the loss is copper plus core.

Symbol	Meaning	Unit
$N_p$	Primary turns	turns
$N_s$	Secondary turns	turns
$n$	Turns ratio	—
$Z_p$	Impedance seen at the primary	Ω

Common mistakes

Expecting a transformer to work on DC.
Induction needs changing flux. On DC the secondary produces nothing and the primary is limited only by its winding resistance, so it overheats.
Confusing the turns ratio for the impedance ratio.
Impedance scales with the square of the turns ratio. A 10:1 transformer is a 100:1 impedance transformation.
Sizing a transformer by watts alone.
Transformers are rated in volt-amperes because they must carry reactive current too. A poor power factor load needs more VA than its wattage suggests.
Ignoring inrush current.
Energising at the wrong point in the cycle briefly saturates the core and draws many times normal current. Use a slow-blow fuse or soft-start.
Assuming no-load means no current.
Magnetising current flows even unloaded, and core loss continues whenever the transformer is energised. It is why leaving them powered wastes energy.

Frequently asked questions

How does the turns ratio affect voltage?

Secondary voltage equals primary voltage times the secondary turns divided by the primary turns. A 10 to 1 step-down transformer converts 240 V to 24 V.

Does a transformer change power?

An ideal transformer conserves power, so stepping voltage down steps current up by the same factor. Real transformers lose some power to winding resistance and core losses, typically achieving 95 to 99 percent efficiency.

How does impedance transform through a transformer?

Impedance scales with the square of the turns ratio. A 10 to 1 transformer makes an 8 ohm speaker look like 800 ohms to the primary, which is how output transformers match valve amplifiers to loudspeakers.

Why can't a transformer work on DC?

Transformer action depends on a changing magnetic flux inducing voltage in the secondary. Steady DC produces constant flux and therefore no induced voltage, while the winding resistance alone limits current and the transformer overheats.

What is inrush current?

Energising a transformer at an unfavourable point in the AC cycle can drive the core briefly into saturation, drawing many times the normal current for a few cycles. It is why transformer circuits use slow-blow fuses or soft-start circuitry.