Transformer vs Inductor for lighting a bulb or any other appliance

Question

There was a question in my school physics exam which is as follows:

Consider a 100W bulb which operates at 50V dc. John wants to light this bulb by a 200V ac source. What component should he use, also give its specifications.

The answer to the question is an inductor, with which I have got no issues. But in the exam, I wrote my answer to be a step-down transformer, which I have myself used for such applications. In the explanation I wrote the following:

A step-down transformer shall be used for this purpose. The specifications would be : 200V/50V (rms). The 50V rms voltage will dissipate the same power as 50V dc in one cycle, so irrespective of the current required, supplying the required voltage will achieve the same results. The winding of the primary and the secondary coils will be in the ratio 4:1 (assuming lossless transmission)

My teacher didn't accept this answer and neither did she give any explanations for why my answer was wrong. Despite having used it myself for the same purpose (powering my ac motors which operate at lower voltages - 12V), my answer was marked incorrect. Why is it so, or is it incorrect at all (since the question was ambiguous, I chose to write transformer as my answer)?

Answer 1

Your answer is a possibility, however if transformers had not been covered it might be considered incorrect. Why not a capacitor, for example. Also it avoided you calculating the reactance at your mains frequency and thus the inductance which was probably the point of the exercise.

I would not consider your answer complete in any case, as you did not specify the VA of the transformer.

Answer 2

I think I understand the rejection of your answer if the transformer is not considered as a component. This apart from extra calculations or VA values. In fact the transformer has a primary coil, a secundairy coil and a magnetic body. Therefore it is not "one" component.

Answer 3

Your instructions were to:

Consider a 100W bulb which operates at 50V dc. John wants to light this bulb by a 200V ac source. What component should he use, also give its specifications.

You glossed over the transformer's specifications and supplied only the stepdown ratio, completely neglecting the primary inductance, the number of turns and wire sizes needed for the primary and secondary, the primary and secondary resistances, the copper and core losses, the magnetic properties of the core and, as Spehro noted, the power factor.

As far as simplicity goes - and since there was no mention of efficiency in the question as you quoted it - my choice would have been a simple 75 ohm non-inductive resistor capable of standing off greater than, say, 283 volts, peak, and being able to dissipate 300 watts continuously, plus the turn-on transient of the [tungsten] lamp.