Confused about transformers formula derivation

In summary, the conversation discusses the equation Vp/Vs = Np/Ns and how it relates to the primary and secondary voltages in a transformer. It is explained that this is due to Faraday's law of induction, where a change in magnetic flux through the primary coils induces a voltage in the secondary coils. The concept is clarified with the help of a transformer diagram from Wikipedia.
  • #1
Math Ematics
3
0
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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  • #2
It is just the Faraday law, which connects the magnetic flux, voltage and turns.
Magnetic flux rate is same for both coils.
 
Last edited:
  • #3
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?
 
  • #4
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.
 
  • #5
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.
 

1. How do transformers work?

Transformers work by using electromagnetic induction to transfer electrical energy from one circuit to another. They consist of two coils, a primary and a secondary, that are wound around a shared iron core. When an alternating current flows through the primary coil, it creates a varying magnetic field that induces a voltage in the secondary coil, thus transferring the energy.

2. What is the formula for transformer voltage?

The formula for transformer voltage is V1/V2 = N1/N2, where V1 and V2 are the voltages in the primary and secondary coils, and N1 and N2 are the number of turns in the primary and secondary coils, respectively. This is known as the turns ratio and determines the voltage ratio between the two coils.

3. How is the transformer formula derived?

The transformer formula is derived from Faraday's law of electromagnetic induction, which states that the induced voltage in a coil is directly proportional to the rate of change of the magnetic flux through the coil. By manipulating this equation and taking into account the number of turns in each coil, the transformer formula can be derived.

4. What is the significance of the transformer formula?

The transformer formula is significant because it allows us to predict and control the voltage output of a transformer. By knowing the turns ratio, we can calculate the output voltage for a given input voltage, enabling us to design and use transformers for various applications.

5. Are there any limitations to the transformer formula?

The transformer formula assumes ideal conditions and does not take into account losses such as resistance and leakage flux. Therefore, it may not accurately predict the actual voltage output of a transformer. Additionally, it only applies to ideal transformers with a constant turns ratio, so it may not be applicable to more complex or non-ideal transformer designs.

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