# Maximum flux in a single phase transformer

• bensm0
In summary, the flux linkage is the integral of voltage, not volts multiplied by time. The flux is simply the flux linkage divided by the number of turns.f

#### bensm0

A single phase transformer has the following rating: 120 kVA, 2000 V/100 V, 60 Hz with 1000 primary turns.

Determine:
(a) the secondary turns
(b) the rated primary and secondary currents
(c) the maximum flux
(d) given a maximum flux density of 0.25 T, the cross-sectional area of the core.

I have answers for A and B, I'm struggling with C and D! Any help greatly appreciated!

Remember emf = -Ndφ/dt?

Could you explain that equation please?

The negative of the time-rate of change of magnetic flux per winding turn, multiplied by the number of turns, equals the electromotive force applied to those turns.

Otherwise known as Faraday's law of induction. Very famous ...

Is dt going to be the reciprocal of the frequency? And will EMF be zero for max flux occurs when transformer is idle? I'm still unsure.

Suppose you have a cosinusoidal voltage V=Vmax*cos(wt). What would be the equation of the flux using this EMF in Faraday's law? What is the magnitude of this flux waveform in terms of V?

Suppose you have a cosinusoidal voltage V=Vmax*cos(wt). What would be the equation of the flux using this EMF in Faraday's law? What is the magnitude of this flux waveform in terms of V?

emf = V = -Ndφ/dt
Oh sorry I didn't realize you were not the questioner.

To be fair, Greek lettered equations usually confuse me at first glance too! Clearer to state just in plain english sometimes! Here is the same again, transliterated:

Magnetic flux (Weber) is the Volts multiplied by [integrated over] the time, divided by the turns.

Or in 'simplified algebra';

Wb=V.s/[turns]

Bear in mind you have to take the average Volts in this formula (Av:RMS = ~1.11) [because we integrate over time], plus the flux is two sided (+ and - flux in each half cycle). (The formula above works fine if you are working with square waves only, but doesn't account for integrating the Volts over the time period being calculated for.)

Also, the 's' is just a half cycle, so if you want to use frequency directly you get the 4.44 term, as used below (2 x 2 x 1.11).

So, as for the cross-sectional area (T=Wb/A), this is generally approximated to the following formula:

T(Peak Flux density, Teslas)=VRMS/{4.44 x frequency x cross-section x turns}

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This is false.
1) The flux linkage is the integral of voltage, not volts multiplied by time. If you do the time integral of the previous voltage waveform, the magnitude of this waveform is the answer to the poster's question. Flux is simply the flux linkage divided by the number of turns.
2) Never answer an homework type question, you have to let them work it out.

This is false.
1) The flux linkage is the integral of voltage, not volts multiplied by time.

Well, to be pedantic, I would say the 'integral of voltage' is physically meaningless, so why use it as a concept in an educational setting? What we are looking at is the rate of change of flux is the Volts/turn at any instant. I'd says any other conclusions are just mathematical machinations after that that don't add much to comprehension of the concepts, which are difficult enough to graps before turning it into pure maths.

I am unclear what you are saying is 'false'. We do not seem to be disagreeing.

2) Never answer an homework type question, you have to let them work it out.

No-one has, yet. I've only sought to provide the basic simplified equations that practical transformer-builders use.

Well, to be pedantic, I would say the 'integral of voltage' is physically meaningless, so why use it as a concept in an educational setting? What we are looking at is the rate of change of flux is the Volts/turn at any instant. I'd says any other conclusions are just mathematical machinations after that that don't add much to comprehension of the concepts, which are difficult enough to graps before turning it into pure maths.

I agree, but if the goal is comprehension of the concepts, then why give the formula (that only works out for a given voltage waveform)? Understanding where that formula comes from is the key in understanding, rather than "plug-and-play".

If the question is about transformer engineering, obviously the author is familiar with integrals. The term "rate of change" is precisely the definition of the derivative. I'm not sure if there is an analog term for the integral, but perhaps it is best to talk about "surface under the waveform", instead of Volts*time. The former is only true for a DC waveform, which we would obviously not like to put on the transformer.

I can answer your question. The formula for Maximum flux = V1= 4.44F∅N1 or V2=4.44F∅N2. Hope that does helps.