Confused about transformers formula derivation

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Discussion Overview

The discussion revolves around the derivation of the transformer equation Vp/Vs = Np/Ns, focusing on the relationship between primary and secondary voltages and the induced electromotive forces (emfs) in the context of Faraday's law of electromagnetic induction. Participants explore the implications of applying voltage to the primary coil and how it relates to the induced emf in both primary and secondary coils.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant expresses confusion about the relationship between the primary voltage (Vp) and the induced emf (ε) in the primary coil, questioning whether Vp can be equated to ε (primary).
  • Another participant states that the magnetic flux rate is the same for both coils, implying a connection between the voltages and turns of the coils.
  • A participant seeks clarification on whether the change in magnetic flux through the primary coils results in an induced emf that counters the applied primary voltage.
  • Another participant reiterates that applying voltage to the primary coil induces a voltage in the secondary coil according to Faraday's law, suggesting that the same magnetic flux applies to both coils.
  • One participant indicates they have gained understanding from the discussion, but does not clarify what specific points were resolved.

Areas of Agreement / Disagreement

Participants express varying levels of understanding regarding the relationship between applied voltage and induced emf, with some agreeing on the application of Faraday's law while others remain uncertain about specific implications. The discussion does not reach a consensus on the interpretation of the primary voltage in relation to induced emf.

Contextual Notes

There are unresolved questions regarding the assumptions made about the relationship between applied voltage and induced emf, as well as the implications of magnetic flux being the same for both coils. The discussion does not clarify the mathematical steps involved in deriving the transformer equation.

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Hi,

I've been a bit confused with how the equation Vp/Vs = Np/Ns came about. From reading a physics textbook, I understand that the voltages came from the emfs ε (primary) and ε (secondary). The primary voltage through the primary coils causes a change in magnetic flux which induces an emf in the secondary coils. From this, I can see why ε (secondary) is equal to Vs, but what I don't understand is why the ε (primary) can be replaced with Vp when the formula for ε (primary) is equal to -N (primary) * delta (flux)/delta (time). I thought this equation is for the induced emf, not the applied voltage from the primary source. Or is the primary voltage equal to an induced emf in the primary coils from iron core ie. if a voltage is applied to a solenoid with N(primary) coils, then would there result in a delta (flux)/delta (time)?

If apply voltage to solenoid, then would applied V= N* (delta flux)/ (delta time)?
which would essentially be the same backwards : induced emf = N* (delta flux)/ (delta time)? Is this true or am I totally wrong?

(ideal wires assumed)

Thank you.
 
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It is just the Faraday law, which connects the magnetic flux, voltage and turns.
Magnetic flux rate is same for both coils.
 
Last edited:
Rajini said:
It is just the Faraday law, which connects the magnetic flux, voltage and turns.
Magnetic flux rate is same for both coils.
Hi Rajini, thanks for replying.

So I'm just wondering, does the change in magnetic flux through the primary coils cause an induced emf equal to the applied primary voltage through the primary coils themselves as well? Would that counteract the voltage from the primary source?
 
Actually when you apply a voltage to primary coil it induces a voltage in secondary according to faraday induction law. Now the magnetic flux is same for both coils..Keeping this in mind you can find the relation for secondary coil..The same applies to primary..equating both the relations you get the famous transformer law..
look into wiki
http://en.wikipedia.org/wiki/Transformer
there you will find explanation with picture.
 
I think I understand now, thanks a lot!


Rajini said:
Actually when you apply a voltage to primary coil it induces a voltage in secondary according to faraday induction law. Now the magnetic flux is same for both coils..Keeping this in mind you can find the relation for secondary coil..The same applies to primary..equating both the relations you get the famous transformer law..
look into wiki
http://en.wikipedia.org/wiki/Transformer
there you will find explanation with picture.
 

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