load-resistance-primary-current-limit-three-row-scan - Electronic Circuits XV & XVI: Transformers and Switched-Capacitor Conversion Step by Step

Secondary load resistance reflects back into the primary current budget, so lower load resistance demands more primary-side current. The 12, 6, and 3 ohm loads give primary load currents 1/4, 1/2, and 1 A against a 1/2 A budget exactly for the ideal turn-ratio model; real transformers add winding resistance, leakage inductance, regulation, core loss, heating, parasitic capacitance, load variation, and current measurement uncertainty.

Secondary load resistance becomes a primary-side current budget. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Load resistance row 1

Transformer voltage ratio stays fixed. Secondary load 12 ohm gives secondary current 1/2 A and primary load current 1/4 A against a 1/2 A budget, so margin is 1/4 A.

m=\tfrac{1}{4}\ \text{A}\quad\text{pass}

Load resistance row 2

Transformer voltage ratio stays fixed. Secondary load 6 ohm gives secondary current 1 A and primary load current 1/2 A against a 1/2 A budget, so margin is 0 A.

m=0\ \text{A}\quad\text{pass}

Load resistance row 3

Transformer voltage ratio stays fixed. Secondary load 3 ohm gives secondary current 2 A and primary load current 1 A against a 1/2 A budget, so margin is negative 1/2 A.

m=\tfrac{-1}{2}\ \text{A}\quad\text{fail}