School Transformer with a Solid Core
A student winds a transformer to operate a 12 V, 24 W lamp from a 230 V, 50 Hz supply. She uses 1000 turns on the primary and calculates 52 turns on the secondary. The core is a solid soft-iron bolt, and the windings are loose. With the lamp connected, the secondary voltage measured by a digital multimeter is 9.5 V, the lamp is dim, and the transformer becomes warm even with no load. The primary current with the lamp on is 0.18 A. The lamp's resistance at operating temperature is about 6 Ω, but its cold resistance is 0.8 Ω. She has another identical bolt, varnish, thicker enamelled wire, and a laminating kit. She must decide whether to change the turns ratio, use a laminated core, or improve the winding, and explain the no-load heating.
1. Calculate the ideal secondary turns and the ideal secondary voltage; compare with 9.5 V and compute the voltage regulation. What does this rule out as the only problem?
Read the worked answer
For an ideal transformer, Ns/Np = Vs/Vp, so Ns = 1000×12/230 = 52.2, i.e. 52 turns. With 52 turns, the ideal secondary voltage is Vs = 230×52/1000 = 11.96 V. The observed 9.5 V is much lower, with regulation (11.96−9.5)/11.96 = 20.6%. The turns ratio is therefore approximately correct; the low reading is not caused by a grossly wrong secondary turns count. It points to voltage drop under load: winding resistance, leakage flux and a poor core. A no-load measurement would separate turns-ratio error from regulation. If the no-load voltage is near 12 V and the on-load voltage is 9.5 V, the turns count is not the main problem and increasing it blindly could overvoltage the lamp at light load.
2. Explain the no-load heating and why a solid bolt is a poor core. How do laminations reduce it, and what other no-load loss remains?
Read the worked answer
The alternating primary current produces an alternating flux in the iron. A solid iron bolt is a continuous conductor, so this changing flux induces large eddy currents in it. Iron has low resistivity, so the eddy currents are large and dissipate I²R heat even when the secondary is open. The bolt also shows magnetic hysteresis, which heats the core once per cycle. Laminations are thin sheets insulated from one another by varnish or oxide. They break the eddy-current paths into narrow loops, greatly increasing the effective resistance and reducing eddy-current loss. Hysteresis loss remains, so a soft magnetic material such as silicon steel is preferable to ordinary iron. Loose windings and a poor core also increase leakage flux, which worsens regulation.
3. The lamp is dim. Rank the following changes: increase secondary turns to 58, use a laminated core, use thicker secondary wire, tighten the windings. Justify with the measurements.
Read the worked answer
The primary input is about 230×0.18 = 41 VA, while the lamp at 9.5 V and 6 Ω takes about 15 W, so the transformer is inefficient and the lost power is heating the core and windings. Increasing the secondary to 58 turns would raise the no-load voltage to about 13.3 V, but it would not remove the regulation; it would risk overvolting the lamp when the load is light. The laminated core should be the first change because it directly addresses the no-load heating and eddy-current loss. Thicker secondary wire is next: at about 2 A, the secondary copper loss is significant, and a thicker wire reduces resistance and improves regulation. Tight windings reduce leakage reactance. After these changes, measure the on-load voltage and adjust turns only slightly if needed.