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A single-phase, 230 V, 50 Hz AC mains-fed step-down transformer (4:1) supplies power to a half-wave uncontrolled AC-DC converter used for charging a 12 V DC battery, with a series current-limiting resistor of 19.04 \(\Omega\). The charging current is

1. 2.43 A
2. 1.65 A
3. 1.22 A
4. 1.0 A

Correct answer: 2.43 A

Solution

A 4:1 step-down transformer gives a secondary RMS voltage of 57.5 V, so the peak is about 81.3 V. For a half-wave battery charger, the average charging current is determined by the portion of the waveform above the 12 V battery voltage through the 19.04 \(\Omega\) resistor, which evaluates to 2.43 A.

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