How Do You Calculate Turns and Current in an Ideal Transformer?

[Physicist3]

Homework Statement

The Mag FLux Density in the core of a 4.4kVA 440V/4400V step up TX is 0.8T (rms). If the induced emf per turn is 10V, find: a) the primary and secondary turns, b) The cross sec area of the core, c) the full load current in each winding.

Homework Equations

The Attempt at a Solution

part a isn't hard, as this question is in a chapter dealing with ideal transformers and so The total emf induced is the same as the applied voltage. The Number of primary turns can therefore be deduced by;

Total emf induced/emf per turn = 440/10 = 44 turns in primary,

this can then be done again for the secondary and the resulting value for number of secondary turn is 440.

For the third part, I believe that the primary current = VA/V1 = 4400VA /440V = 10A, anf the secondary current = VA/V2 = 4400VA / 4400V = 1A. This would make sense based on all the above calculations for turns etc.

I would like some help with the second part of the equation, as i cannot understand how it can be solved using the emf equations for a single phase transformer, as there is no frequency given??

Thanks

 

[rude man]

Homework Statement

The Mag FLux Density in the core of a 4.4kVA 440V/4400V step up TX is 0.8T (rms). If the induced emf per turn is 10V, find: a) the primary and secondary turns, b) The cross sec area of the core, c) the full load current in each winding.

Homework Equations

The Attempt at a Solution

part a isn't hard, as this question is in a chapter dealing with ideal transformers and so The total emf induced is the same as the applied voltage. The Number of primary turns can therefore be deduced by;

Total emf induced/emf per turn = 440/10 = 44 turns in primary,

this can then be done again for the secondary and the resulting value for number of secondary turn is 440.

For the third part, I believe that the primary current = VA/V1 = 4400VA /440V = 10A, anf the secondary current = VA/V2 = 4400VA / 4400V = 1A. This would make sense based on all the above calculations for turns etc.

I would like some help with the second part of the equation, as i cannot understand how it can be solved using the emf equations for a single phase transformer, as there is no frequency given??

Thanks

You have to assume a frequency. Probably 60 Hz. Good point!

 

[Physicist3]

You have to assume a frequency. Probably 60 Hz. Good point!

This is what I thought, but obviously there are two feasible frequencies that could be used (50Hz or 60Hz), so the accuracy of the answer will therefore be affected. I hate it when textbooks don't give answers to their questions!

 

[rude man]

This is what I thought, but obviously there are two feasible frequencies that could be used (50Hz or 60Hz), so the accuracy of the answer will therefore be affected. I hate it when textbooks don't give answers to their questions!

Agreed! Where was your textbook published? That might offer a clue as to the intended frequency. What about context (the chapter associated with the problem)?

 

[rezeew]

for your question.

For part b, the cross-sectional area of the core can be found using the equation B = (μ0μrN)/A, where B is the magnetic flux density, μ0 is the permeability of free space (constant value), μr is the relative permeability of the core material (can be found in a table), N is the total number of turns, and A is the cross-sectional area of the core.

Since all the values in this equation are known except for A, we can rearrange it to solve for A:

A = (μ0μrN)/B

Substituting in the given values, we get:

A = (4π x 10^-7)(μr)(44) / 0.8 = 1.76μr m^2

So, the cross-sectional area of the core is 1.76 times the relative permeability of the core material.

For part c, your calculations for the primary and secondary currents are correct. The frequency is not needed in this case because the induced emf per turn is given in the problem, so we do not need to use the emf equation for a single phase transformer (which includes frequency).

I hope this helps!