Finding Turns in Transformer

TURNS AND VOLTAGE RATIOS

The ratio of 0.31 V per turn will apply to primary/secondary winding.

Well, I could be wrong, but the above postulate comes logically to mind.

Whoops sorry I made an incorrect observation.

Correction

78/245= 0.31V x 3 = o.93V

Right final answer, but with a superfluous "correction" along the way.

76 ÷ (0.93/3) ≈ 245 turns.

245...........250................251, What EVER it takes.

The key information needed for any transformer computation is the turns/volt number. To get that using the information provided, we take the reciprocal of 0.31 V/T. Which will be = to 1/V/T = 1/0.31= 3.22

The turn ratio of 3.22 can now be used as the constant to get the number of turns needed for the primary, which is = 1548 truns, and for the primary which will be = 386 turns.

The KVA rating is needed to determine the proper AWG size for the magnet wire that can safely carry the rated current in amperes. It is also needed to determine the size of the core area among other things.

The teacher was trying to see who really understood the concepts of turns and voltage ratios by deliberately putting multiple turns and voltage ratios into the problem.

Assuming the same transformer but instead of a 3-turn coil with 76 V and 0.93 V, he had instead said a 1-turn coil with 245 V and 1 V measured, it would have been obvious (hopefully) that both the turns and voltage ratios were 245 to 1.

The teaching problem is that if he then threw the original problem statement into a quiz only those students that truly understood the concept might possibly get it right, so in effect he was helping students such as yourself who needed a bit of assistance figure things out (see, it worked).

By the way, if you want to communicate effectively, drop the slang/texting/poor grammar and proofread your work, it will help others feel more like helping you.

Good luck in your studies.

Another approach is to use the volts per turn under the test conditions...

Secondary - 76 volts at 0.31 volts/turn gives 76/0.31 = 245 turns.

Primary - must have 245 x 480/120 = 980 turns.

With a real transformer , it would be advisable to measure the primary voltage during the test. The question does not give any frequency [rated or test] or standard specification - so the turns ratio being the same as the nameplate voltage ratio is just an assumption. The name plate voltage rating could be at rated load, the zero-load voltage being higher to make up resistive & inductive voltage drops caused by load current.

For testing a turns ratio you can use any convenient voltage which is less than the rated voltage or greater by a small margin say 5%. A voltage too high could cause magnetic saturation. This could cause waveform distortion of the test source due to overloading, or distorted transformer output. Likely, the voltmeter would no longer give a true reading because input and output had different waveforms.

The basic assumption is that the same magnetic flux is passing through both windings so the fundamental equation :-

induced voltage = N x rate of change of magnetic flux. (1)

where N is the number of turns on a winding.

- is true for both windings, so their voltages must be in proportion to their turns.

Note it is also assumed that the induced voltage in the primary equals the supply voltage, so there is zero current in the primary.

In many real transformers, the assumption that

1. all the primary flux links the secondary
2. the primary current is zero at rated voltage, zero secondary load

is a very useful approach, although inaccurate on test or careful theoretical analysis which includes the effect of winding resistance voltage drops and that setting up an alternating flux in a transformer or inductor requires some current.

As example, I would note that I have tested two single phase 230V AC 50 Hz input transformers on "no-load", one a 24V 0.2 amp AC output "plug-top" type: the other a toroidal 30V 60 VA item in a Hi-Fi sound amplifier.

The first had 56 mA primary current, while the second was 5 mA despite being over 10 times the rating. This primary current is the "magnetizing" current necessary to produce the working magnetic flux. Note that the plugtop absorbed 3.3 watts (all heating it up) even on no-load, compared to its 4.8 watt output rating and 0.056 x 240 = 13.4 volt-amps input no-load.

The plugtop had 30V out at no-load (poor voltage regulation, no-load to rated current, due to high winding resistance) while the toroidal was about 32V.

The difference is largely that the plugtop is made for minimum cost using the minimum amount of iron and copper while the toroid is designed for good regulation of its output voltage while minimizing size and weight (and external magnetic field, which is heard as "hum" on the sound).