current-ratio-keeps-power - Electronic Circuits XV & XVI: Transformers and Switched-Capacitor Conversion Step by Step

A current-ratio-keeps-power scan holds the voltage ratio fixed and varies the secondary current across three rows, checking that the primary current rises through the inverse turns ratio so P_p = P_s closes row by row. The arithmetic is exact only for the stated currents, voltages, powers, turns counts, and rows in the ideal lossless, perfectly coupled transformer model. Real transformers add winding resistance, leakage flux, core losses, magnetizing current, frequency rolloff, probe/calibration limits, finite precision, and measurement uncertainty.

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}