Home > transformer > Induced voltages and flux within a transformer and their polarities

# Induced voltages and flux within a transformer and their polarities

May 15Hits:3

This is a multifaceted question, and is more to see if I understand what happens inside a transformer. I understand the general idea behind transformers: Alternating voltage that is applied to the primary is "mirrored" at the secondary and its size is dependent on the ratio of turns. However, the polarities of the induced voltages and "cancelation" of flux within the core is a little confusing to me. So let's start at the beginning:

Applying a sinusoidal voltage, \$V_{AC} = V\sin(\omega t)\$, to the primary causes current \$i_p\$ to flow through it. We can see that \$i_p\$ is proportional to \$-\cos(\omega t)\$, and so is the flux \$\phi_1(t)\$. Since the flux intercepts the primary coil, it induces a voltage in the primary, and according to Lenz's law, that voltage will point in the direction that opposes the change that caused it. In other words, if we denote this new voltage by \$V_p\$, then

$$V_p = -n_p\frac{d\phi_1}{dt},$$

where \$n_p\$ is the number of turns in the primary. We see that \$V_p \sim -\sin(\omega t)\$, so \$V_p\$ points in the opposite direction to \$V_s\$. The two opposing voltages are why \$i_p\$ is very low when the transformer isn't loaded. Also, if they had canceled each other completely we'd have no current and therefore no flux. Is all of this correct so far?

Now we attach a load to the secondary, and the same flux, \$\phi_1\$, induces a voltage in the secondary, and it is $$V_s = -n_s \frac{d\phi_1}{dt},$$ where \$n_s\$ is the number of turns in the secondary.

Like, \$V_p\$, \$V_s \sim -\sin(\omega t)\$, and this is where it gets tricky for me. The voltage that comes out of the secondary should have the same phase and polarity as the voltage that is fed into the primary. What I get here is that they have opposite polarities! Additionally, it is not clear to me how we physically decide on the polarity of the secondary's leads, what's \$+\$ and what's \$-\$? Then there's also the way the two coils are wound which also affects the polarity.

One way for me to settle this is to think of Lenz's law again. If we denote the current induced in the secondary as \$i_s\$, then Lenz says that \$i_s\$, being induced by \$\phi_1\$, will flow to oppose the change that induced it. I take this to mean that \$i_2\$ will flow in such a way that the flux it generates, \$\phi_2(t)\$, will oppose \$\phi_1\$. So no matter how the secondary coil is wound (CW or CCW), the induced current, \$i_2\$, will "arrange" itself so that \$\phi_2\$ will oppose \$\phi_1\$. Depending on what the secondary is wound, the polarity of this signal will change, as this diagram shows.

Am I correct so far? If yes, then why do we choose the "top" lead to have the positive polarity? And how do we square the whole business with the induced voltage, \$V_s\$ having the reverse polarity to the source voltage that feeds the transformer?

Now comes another part I'm not sure about. \$\phi_2\$ acts against \$\phi_1\$, therefore reducing it and reducing \$V_p\$, so the primary draws more current from the source. Therefore \$\phi_1\$ gets big again, and I assume it more or less cancels the reverse flux \$\phi_2\$, so really \$V_p\$ doesn't exist across the primary. I've seen several places say that the transformer wants to maintain the high flux in the core. Is this why?

Lastly, is it just me or Faraday and Lenz's laws are really just for illustration purposes? I don't think that what happens inside the transformer is reactionary like that where one current flows and then another reacts to it. For instance, we don't see a reverse flux, but breaking it down this way helps us understand why the end result is the way it is.

To answer your questions: We don't choose anything with transformers to have positive polarity. See the wiki. You could reverse the dots on both sides and still get the same result. The dots help you to know what the physical relation of the transformer coils are. If you have two coils, you have four terminals to connect to the circuit. But the circuit doesn't care which side is positive or negative. It only cares if the coils are reversed or not. It is just a notation. Notations are only useful if you know the rules behind them and how they are realized in the model and the physical world.

As far as magnetic flux goes, you really need to think about the magnetic fluxes in terms of

. The transformer model uses 4 inductances, 2 of which are mutual (usuually called M) and characterize the flux between the two inductors. Vp always exists across the primary, you have to have a voltage to have current, it may be zero if its a time varying field.

Maintaining high flux in the core applies to non-ideal transformers. An ideal transformer has no resistance in the coil and no magnetic resistance in the material of the core. The idea there is if you introduce a material you have losses, you also have losses to outside world. In a universe with only a transformer, all the field lines would loop back into the other end, and you would have no losses. In the real world they connect and do work on other materials. In addition, air is not a great way to conduct magnetic fields, it has a low magnetic permeability. So we use a good material like iron to conduct the most of the magnetic field with its high magnetic permeability. This also has its problems because iron saturates, it has a point where it can't conduct very well. This saturation must be taken into account or it will clip the top of the sine wave.

I think a better way to look at a transformer is you are trading off voltage for current. A power engineer might be concerned about the inner workings of a transformer where you have losses (and they actually have magnetic circuits with multiple coils) but in the ideal case all you have to worry about are the mutual inductance, the inductance of the coils themselves and the ratio of the coils.

And the last paragraph doesn't make much sense to me either. So I can't answer your question there.

## Related Articles

• ### Induced voltages and flux within a transformer and their polaritiesMay 15

This is a multifaceted question, and is more to see if I understand what happens inside a transformer. I understand the general idea behind transformers: Alternating voltage that is applied to the primary is "mirrored" at the secondary and its s

• ### Polarity of the induced voltage on inductor for an applied magnetic flux according to the Lenz's LawMay 3

I'm trying to visualize the Lenz's Law on a practical inductor. The Lenz's Law says that $$\mathcal{E} = -\dfrac{\partial \Phi}{\partial t} .$$ Now, assume that there is a magnetic flux inside the coil is in the given direction in the image below,

• ### Why is maximum flux attained in transformer when off load?May 30

Can anyone explain to me why the maximum flux in a transformer is attained when off load? What happens to the flux when on load? Are the flux from the secondary load current and primary load current just leaking out into space? Or are the magnetic pa

• ### Mutual Inductance - Self Induced VoltageMay 18

When constructing mesh equations for each loop where two coils are linked, I know how to determine the polarity of the induced voltage by use of dot markings, but I need some clarification on the self induced voltage... If I take the current as clock

• ### How to calculate the induced voltage?August 26

From the given diagram: Conductor(C) is the only movable part with given velocity (v), connected to a stationary terminals(top & bottom) and an exterior circuit with a load. Will current flow to the load? Or only around the conductor? Is the voltage

• ### generate high voltage using LM555 with a transformerDecember 30

I'm a French student (please forgive my bad English spelling) who works on a system of portable echograph (you can find the information of the project on the wiki of echopen). Could you help me please? I would like to generate a tension of 100V. Firs

• ### Doubt on induced voltageJune 19

Honestly, this is a homework question. Below you could see the description of the question Here you have the relevant answer. My argument Here we can neglect answer number 1 and 4 Reason : According to the given diagram we can say current travels for

• ### How to calculate the Induced Voltage Given Spinning Conducting Loop? Intro to Electromagnetics problemSeptember 17

I'm having trouble figuring out a different variation of this problem. On my homework, I'm asked to find the induced EMF for the following B field: $$\vec{B}=50\vec{a_y}$$ I was able to figure out the problem with the B field being: \vec{B}=50\vec{

• ### Which resistor should I pick among "several resistors "under voltage source, when using source transformation method?December 19

I got stuck solving source transformation problem , I am sure that the second circuit is obtained after apllying 2 source transformations. As You can see in this example, the 30 Volt Voltage source becomes 300 Volt Voltage source using Source transfo

• ### Effects of changing the frequency of a transformerDecember 20

If the frequency of a transformer is decreased by keeping voltage same, then what will be the new KVA rating, magnetizing current and inductance, the induced voltage and loss of the transformer? --------------Solutions------------- I'll assume that y

• ### How does flux exist in a transformer?May 5

What I understand about working principles of ideal transformer: We apply an alternating voltage at the primary side. This creates a flux inside the transformer core (\$\Phi_p\$). Some voltage is induced on the secondary side winding according to the

• ### Transformer primary and secondary voltage phase shiftSeptember 6

If we apply a voltage at the primary terminals of a transformer then for this we can get a voltage at the secondary. But they have 180 degree phase difference. What is the reason behind this?? I want to know why the phase difference between primary v

• ### How do I use a transformer as an inductor?June 14

Lp: Self inductance of the primary winding. Ls: Self inductance of the secondary winding. Lm: Mutual inductance between the primary and secondary windings. Assume that I need an iron core inductor with large inductance to use under 50Hz or 60Hz. How

• ### Current transformer as Sensor, can it sense rectified DC current?July 17

I have been using an inductor around a 230V AC wire ground-side of the switch to check for current in a wire, it is part of control mechanism. I have to add a rectifier now, so occasionally the current will be ~400V DC when rectified, and it has to b

• ### How does a transformer transmit power from the primary to the secondary?April 14

I'm trying to get my head wrapped around transformer operation and in the process regretting the times I snoozed in my Electromagnetics class as a EE student back when I was a lad :) I'm looking for an intuitive understanding, but not just an analogo

• ### Is it possible to have voltage across an inductor without having current through it?April 30

Example : In certain cases in transformers we do assume so having zero current in the secondary but there is still a voltage across it due to mutual flux . Also we do similar things while calculating the thevenin equivalent of the secondary in the tr

• ### Can anyone explain why a B-H curve with Hysteresis doesn't result in a highly non-linear input-output transfer function for a transformer?June 29

See the attached picture of a typical hysteresis loop, it is clearly highly non-linear even if you keep the signal small enough to stay out of the saturation region (beyond points b,e). So my question is why does this not result in a non-linear trans

• ### The \$I^2R\$ loss in transformer is eddy current loss or copper loss?July 29

As the title say, this is what my text book say. I use Hughes Electrical Electronic Technology 10th edition The varying flux in the core induces e.m.f.s and hence currents in the core material. These give rise to \$I^2R\$ losses. These losses are cal

• ### Help understanding transformer AUX windingDecember 31

I'm new here and I'm looking for someone to help clarify the AUX winding of a transformer, more specifically in a switched psu. I see schematics where it's being used either as feedback or voltage input to an ic on the primary taken from a winding on

• ### Direction of flow of current in secondary circuit in AC transformer/rectifierJanuary 10

In this transformer/rectifier if the current in the primary circuit is clockwise what will be the direction of current in the secondary circuit?Why? I'm feeling a bit confused about the direction of flow of current due to flux linkage of primary coil