# Classical Physical Explanation for Turn Ratio in Transformer

• scipioaffric
In summary, the ratio of the number of turns in a transformer is crucial in converting an input voltage to an output voltage because it determines the amount of magnetic flux linkage and thus the inductance. This allows for a more efficient way to control the area exposed to the magnetic field, resulting in a change in voltage. This process is known as electromagnetic induction, and can be further explained using Maxwell's Equations and calculus.

#### scipioaffric

Hello. I'm trying to understand why, in terms of Maxwell's Equations, the ratio of the number of turns in a transformer converts an input voltage to an output voltage. EE explanations only seem to go as deep as this article: http://en.wikipedia.org/wiki/Transformer#Basic_principles

They state that the ratio of the input voltage to output voltage is determined by the number of turns in the primary and secondary coil. But why? What's actually happening to various field lines to change voltages?

Have you studied electromagnetic induction?

Yes, but not in the usual way.

I'm familiar with maxwell's equations and all of that notation, I'm just trying to analyze this part in those terms.

I'm looking for someone to explain in terms of the mechanisms of induction, preferably with calculus.

Is there a way I can further refine the question to get more help?

scipioaffric said:
Hello. I'm trying to understand why, in terms of Maxwell's Equations, the ratio of the number of turns in a transformer converts an input voltage to an output voltage. EE explanations only seem to go as deep as this article: http://en.wikipedia.org/wiki/Transformer#Basic_principles

They state that the ratio of the input voltage to output voltage is determined by the number of turns in the primary and secondary coil. But why? What's actually happening to various field lines to change voltages?

An alternating current will create magnetic and electric field components around the wire. Magnetic field component produced by input is transferred (carried like waveguide) to secondary winding (output) via a ferromagnetic core. Inversely, secondary winding is exposed to magnetic fields carried by ferromagnetic core and induces back a current at open terminals of output. Core is the physical link to carry magnetic fields. Turn ratios determine voltage ratio because at each turn you roll more, you will be exposing more wire length to the magnetic field.

The heart of the matter is magnetic flux linkage. Induction is the process where a magnetic field changing in time across some area in space gives rises to a curling electric field along the edge of that area (the electric field lines literally curl around in a circle). If you happen to have a conducting wire loop placed along the edge of that area containing, which by definition contain free charge, the curling electric field will exert a force on the charges, driving a current through the wire. The key is the amount of magnetic field changing across the area spanned by the loop of wire - the magnetic flux linkage. If you increase the area spanned by the loop of wire, but leave everything else the same, you increase the flux linkage, and thus the inductance. But instead of using ever bigger loops of wire to get more induction, you can also stack loops. Two loops of wire sitting next to each other in a uniform changing magnetic field have as much flux linkage as two loops stacked on top of each other. This is a very space saving way to control the area exposed to the field, and thus the flux linkage: coil a wire so that you make a stack of loops. If you have 20 turns on a coil, you are stacking 20 loops, and thus have 20 times the area and the inductance on a single loop.

## 1. What is the classical physical explanation for turn ratio in transformers?

The classical physical explanation for turn ratio in transformers is based on Faraday's Law of Electromagnetic Induction. According to this law, when a changing magnetic field passes through a conductor, it induces an electric current in the conductor. In a transformer, the primary coil creates a changing magnetic field when an alternating current is passed through it. This changing magnetic field induces a current in the secondary coil, resulting in a voltage being produced in the secondary coil. The turn ratio, or the ratio of the number of turns in the primary coil to the number of turns in the secondary coil, determines the voltage output of the transformer.

## 2. How does the turn ratio affect the voltage output of a transformer?

The turn ratio has a direct impact on the voltage output of a transformer. The voltage output is directly proportional to the turn ratio, meaning that an increase in the turn ratio will result in a higher voltage output, and a decrease in the turn ratio will result in a lower voltage output. This is because a higher turn ratio means that there are more turns in the secondary coil, resulting in a stronger induced current and a higher voltage output.

## 3. Can the turn ratio be changed in a transformer?

Yes, the turn ratio can be changed in a transformer by adjusting the number of turns in the primary and secondary coils. This can be done by physically adding or removing turns from the coils, or by using a tap changer which allows for the turn ratio to be adjusted without physically altering the coils. However, changing the turn ratio can also affect other properties of the transformer, such as its efficiency and impedance.

## 4. How does the turn ratio affect the efficiency of a transformer?

The turn ratio has a direct impact on the efficiency of a transformer. A higher turn ratio results in a higher voltage output, but it also means that more energy is lost in the form of heat due to resistance in the coils. This decreases the efficiency of the transformer. On the other hand, a lower turn ratio means a lower voltage output and less energy lost as heat, resulting in a more efficient transformer.

## 5. Why is the turn ratio important in transformer design?

The turn ratio is an important factor in transformer design because it determines the voltage output of the transformer. This, in turn, affects the overall performance and efficiency of the transformer. In order to meet the specific voltage requirements of a particular application, the turn ratio must be carefully selected and designed. Additionally, the turn ratio also affects other important parameters of the transformer, such as its impedance and current capacity, making it a crucial aspect of transformer design.