current-ratio-keeps-power - Electronic Circuits XV: Transformers and Coupled Inductors Step by Step

Ideal transformer current moves in the inverse turns ratio. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Ideal transformer power is a two-side ledger

The voltage ratio is already fixed. Changing secondary current changes both winding powers together.

P_p=V_pI_p\quad;\quad P_s=V_sI_s

More secondary current asks for more primary current

The same ideal transformer converts the load current back to the primary side.

\begin{array}{c|c|c|c}I_s&I_p&P_s&P_p\\1\ \text{A}&\tfrac{1}{2}\ \text{A}&6\ \text{W}&6\ \text{W}\\2\ \text{A}&1\ \text{A}&12\ \text{W}&12\ \text{W}\\4\ \text{A}&2\ \text{A}&24\ \text{W}&24\ \text{W}\\\end{array}

Inverse current ratio keeps ideal power equal

The current labels are not optional: the checked row binds both powers to the same transformer source.

6\ \text{V}\cdot4\ \text{A}=12\ \text{V}\cdot2\ \text{A}=24\ \text{W}