# transformer current vs ratio

Discussion in 'General Electronics Chat' started by skt, Jul 31, 2012.

1. ### skt Thread Starter New Member

Jul 31, 2012
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0
I am confused now:

Assume I use a iron core for a transformer, ratio is one, inductance is 10mH.

the primary is SERIES with 100 ohm resistor, and secondary has 1K ohm as the load.

If I apply 100V AC(50Hz) to primary and 100 ohm resistor, the primary current will be (100-Ldi/dt)/100. Let's assume the final answer is 0.8A

The ratio is one, I should get 0.8A current at output winding. But the load is 1K, so I will not see 0.8A current at output because it will be 800V cross secondary winding.

Any explanation? Thanks.

2. ### crutschow Expert

Mar 14, 2008
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Yes, you are confusing magnetizing current with load current. The inductance of the transformer determines the primary magnetizing (reactive) current. This current is simply a result of the primary voltage and frequency, and the primary core inductance. This current is not transferred to or seen by the secondary but it does provide magnetic flux which generate the secondary voltage. It is the secondary load current that is carried by the magnetic flux back to the primary (as determined by the turns ratio) which causes the primary load current. The primary load current is in addition to, but out of phase with, the magnetizing current.

What happens when you draw secondary current is that it flows in a direction such as to opposite the primary flux (if you look at the primary and secondary voltage polarities and current directions you will see how that happens). This reduction in flux then reduces the back EMf in the primary, causing more primary current to flow to maintain the core magnetic flux value. That is how an increase in secondary current causes an increase in the primary current.

Make sense?

3. ### mlog Member

Feb 11, 2012
276
36
The thought never would have crossed my mind to use Ldi/dt except in a transient situation or when there is a discontinuity in current. Unless I'm missing something, this is a straight forward, steady state problem.

4. ### crutschow Expert

Mar 14, 2008
20,272
5,738
True. I didn't get into that because it wasn't critical to my explanation, but the normal way to calculate the input magnetizing current would be to use steady-state phasor analysis and not differential equation transient analysis.

5. ### skt Thread Starter New Member

Jul 31, 2012
2
0
Thank you.

I still don't know the terms" steady state". Why cannot use Ldi/dt?

If steady state analysis, how do you determine the actual rms current by math?.

Thanks.

6. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
790
The steady state solution can also be found using complex numbers.

Neglecting other unspecified parameters, the equivalent circuit looking into the primary of the proposed transformer would comprise the magnetizing inductance [10mH] in parallel with the referred secondary load resistance. With a 1:1 ratio the referred secondary load would be the same - 1kΩ.

The 100V 50Hz source would then see the 100Ω primary resistance in series with the parallel combination of the 10mH magnetizing inductance and the 1kΩ referred load.

At 50Hz the inductive reactance would be ωL=2*π*50*10E-3=3.1416Ω

So the primary current Ip would be

$I_p=\frac{V_s}{Z_{tot}}=\frac{100\angle{0^o}}{100+j3.1416 || 1000}$

or

$I_p= \frac{100 \angle{0^o}}{100.01+j3.1416}$

$I_p= 0.9994 \angle{-1.799^o}$ [Ampere]

So it turns out the magnetizing inductance is so low that in this instance it swamps the outcome in relation to the reflected load resistance. The overall effect then being that the series 100Ω on the primary side is the dominant determinant of the primary current.

The secondary current magnitude turns out to be about 3.14mA. Which is nowhere near the primary current of about 1A.

Last edited: Aug 2, 2012
7. ### crutschow Expert

Mar 14, 2008
20,272
5,738
You can use Ldi/dt but it requires the solution of some messy differential equations. Much easier to use phasor algebra with complex numbers as t_n_k described.

8. ### jayaram New Member

Aug 3, 2012
2
2
I have uploaded an image for the circuit you described - I couldn't upload the circuit of this format. Go to http://www.docircuits.com launch the editor and try this circuit. Check what the output is for various resistances and verify if they are correct from Ohm's law formula. You can verify how the primary current varies due to secondary current too.

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