load-reflects-by-turns-ratio-squared - Electronic Circuits XV: Transformers and Coupled Inductors Step by Step

The input equivalent load is a checked turns-squared ledger. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Reflected load uses the square of the turns ratio

The secondary load is cited through the transformer source. The primary equivalent is not a copied caption.

R_p=R_s\left({N_p\over N_s}\right)^{2}

A larger secondary load reflects to a larger primary load

The turns ratio stays fixed while the secondary resistance changes.

\begin{array}{c|c|c|c}R_s&R_p&I_s&I_{p,\text{load}}\\3\ \text{ohm}&12\ \text{ohm}&2\ \text{A}&1\ \text{A}\\6\ \text{ohm}&24\ \text{ohm}&1\ \text{A}&\tfrac{1}{2}\ \text{A}\\12\ \text{ohm}&48\ \text{ohm}&\tfrac{1}{2}\ \text{A}&\tfrac{1}{4}\ \text{A}\\\end{array}

A load reflects by the turns ratio squared

The primary-side equivalent is checked against the cited transformer row, not merely against matching numbers.

R_p=R_s\left({N_p\over N_s}\right)^{2}=3\ \text{ohm}\left({4\over2}\right)^{2}=12\ \text{ohm}