step-down-load-raises-primary-current - Electronic Circuits XV & XVI: Transformers and Switched-Capacitor Conversion Step by Step

A step-down-load-raises-primary-current scan starts from secondary load power and reflects it to the primary, checking that the lower secondary voltage with higher secondary current becomes the primary load current through I_p = P_s / V_p row by row. The arithmetic is exact only for the stated turns counts, voltages, currents, powers, load resistances, and rows in the ideal transformer, perfect-coupling, no-magnetizing-current model. Real transformers add winding resistance, leakage inductance, core loss, magnetizing current, load tolerance, probe/calibration limits, finite precision, and measurement uncertainty.

Secondary load current reflects back to an exact primary current. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

A step-down load current reflects back to the primary

The secondary load sets secondary current first. The transformer then maps that power to primary current.

P_s=V_sI_s\quad;\quad I_{p,\text{load}}={P_s\over V_p}

Lower secondary resistance raises primary load current

The transformer is fixed. The secondary resistance rows change load current and power.

\begin{array}{c|c|c|c}R_s&I_s&I_{p,\text{load}}&P\\9\ \text{ohm}&1\ \text{A}&\tfrac{1}{2}\ \text{A}&9\ \text{W}\\6\ \text{ohm}&\tfrac{3}{2}\ \text{A}&\tfrac{3}{4}\ \text{A}&\tfrac{27}{2}\ \text{W}\\3\ \text{ohm}&3\ \text{A}&\tfrac{3}{2}\ \text{A}&27\ \text{W}\\\end{array}

A low secondary load sets an exact primary load current

The fractional primary current is pinned as an exact rational value.

3\ \text{A}\rightarrow\tfrac{3}{2}\ \text{A}\quad P=27\ \text{W}