Homework Help: Single phase transformer

1. Apr 16, 2012

oxon88

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

V2/V1 = N2/N1

2. Apr 16, 2012

oxon88

trying to work out the answer for part a

N2 = N1*V2 / V1

= (1000 * 100) / 2000

N2= 50 turns

Is this correct?

3. Apr 16, 2012

Staff: Mentor

1000 turns : 50 turns ≡ 2000V : 100V

4. Apr 16, 2012

oxon88

Thanks, can you offer any advice on solving part b?

Im stuck trying to work out the current in either N1 or N2

once i have one of these values I guess i can use V2/V1 = N2/N1 = I2/I1

5. Apr 16, 2012

oxon88

ok here is an attempt at b

I1=120000/2000 = 60A

I2 = 60/0.05 = 1200A

how does this look?

Last edited: Apr 16, 2012
6. Apr 16, 2012

Staff: Mentor

What does it mean when it says a single phase transformer has the following rating: 120 kVA?

7. Apr 16, 2012

oxon88

120kVA is the maximum power the transformer can output. its a measure of volt-amps.

so... 120kVA / 100v = 1200A on the secondary?

8. Apr 16, 2012

Staff: Mentor

Close enough.
Yes. And the same idea applies to the primary, too.

9. Apr 17, 2012

oxon88

I'm a bit stuck with part c. Any advice on this one?

10. Apr 17, 2012

Staff: Mentor

What equations do you know that involve magnetic flux?

11. Apr 18, 2012

oxon88

Would this be appropriate to use?

Magnetic Flux = B.A.cosθ

12. Apr 18, 2012

Staff: Mentor

Φ=B.A.cosθ is a good equation to memorize, and we'll need that for part (d) which relates flux to flux density and area.

For part (c) we need an equation relating flux, voltage and number of turns for a transformer.

13. Apr 18, 2012

oxon88

ok I see. Would this be more appropriate?

Φ = V × T / N

Φ = Flux (weber)
V = Voltage
T = Time
N = No. of turns

Last edited: Apr 18, 2012
14. Apr 18, 2012

Staff: Mentor

In an operating transformer the flux is constantly changing, and in a sinusoidal manner. It's the changing flux linking the secondary that induces the secondary voltage.
You're getting close. It's based on that, but others have done all the necessary fiddle-factoring and you've almost certainly been presented with the final equation in lectures or textbook reading.

Hint: there's a 4.44 factor in it.

Last edited: Apr 18, 2012
15. Apr 18, 2012

oxon88

right then I think I may have got it...

Vp = 4.44 * f * Np * Φmax

2000 = 4.44 * 60 * 1000 * Φmax

2000 = 266400 * Φmax

2000 / 266400 = Φmax

Φmax = 7.51 mWb

16. Apr 18, 2012

Staff: Mentor

17. Apr 18, 2012

oxon88

Great thanks for you help and advice. Its making more sense now. Last part to go.....

Φ = B * A * cosθ

would θ = 0 ?

7.51x10-3 = 0.25 * A * cos(0)

7.51x10-3 / 0.25 = A

A = 0.03003mm2

18. Apr 18, 2012

Staff: Mentor

19. Apr 18, 2012

Staff: Mentor

EDIT: Oops. Misread the Greek. :tongue:
Yes, windings are perpendicular to the core.
Check those units.

20. Apr 18, 2012

oxon88

would it be m2? (standard SI base unit)