# ${}$Self-induction in transformer

Wont self-induction ruin the working of a transformer?

While increasing voltage (AC) in the primary coil, wont there happen a self induction in the primary coil itself?

$$E_0 = -L \frac{dI}{dt}.$$

If there happens a change in current it should cause an emf. Even if the inductance is small. There happens a back emf in the coil.

• The 'self-inductance' of a transformer is the effect of inductance on the primary circuit. It is undesirable insofar as creating a 'lag' between the applied voltage and the resulting current, which has a negative effect on power factor. This means that the full rating of the electrical equipment (wires, etc) is not being utilitised for transferring 'real' power, so there will be some loss in efficiency.
– theo
Dec 3, 2014 at 3:47
• @theo, that should be an answer, not a comment, no? Also, impedance matching is usually addressed by adding compensating elements to the circuit, isn't it? Dec 3, 2014 at 11:20

The self-inductance of a transformer is the net inductive effect reflected onto the primary circuit by the transformer windings. Both the primary and secondary windings of a real transformer exhibit electrical resistance due to copper losses, and inductance due to magnetic flux leakage. Although most of the magnetic flux is confined to the core of the transformer, some flux links one winding without linking the other (leakage flux). The effect can be modeled as primary impedance and secondary impedance 'transposed' to the primary side of an 'ideal' transformer, along with the mutual inductance (magnetisation) and core losses (typically due to eddy currents and hysteresis).

The net effect on the current-voltage relationship through a transformer due to leakage flux is represented by a 'self-inductance'. In large power transformers, the winding resistance is generally large compared with the self-inductance, although the value of self inductance is generally not large compared to the mutual inductance, particularly at full load. When lightly loaded (<50%) the self inductance can have a noticeable effect in terms of a 'lag' between the applied voltage and the resulting current. This can be seen as 'undesirable' from an economic point of view, since it results in a low 'power factor'. This effectively means the full rating of the electrical transformer and related equipment (wires, switches, etc) are not being utilitized to their maximum capacity for transferring 'real' power, so there is some loss in efficiency.

On the other hand, the effect of self-inductance reduces the prospective fault currents. These are the potentially large electric current which flows when there is a fault, such as a short circuit between the line and earth ground. This reduces the need for large 'oversized' cables to handle a high fault current and also reduces the risk of possible damage caused by such currents.

• Magnetic flu sounds scary :) Dec 3, 2014 at 17:28

Forget for a moment the secondary coil. Then you do indeed get an EMF as you describe. This is called an inductor, and it's hallmark is that current and voltage are out of phase by 90 degrees, i.e. the voltage drop across the inductor is $L \frac{dI}{dt}$. This does not ruin the transformer, as you say, because it merely means that if the voltage across the transformer is $V_0 \cos\omega t$ then the current is $I = \frac{V_0}{L} \sin\omega t$.

I should clarify something about inductors, that was hinted at in theo's comment. Consider an inductor that is placed in parallel with a perfectly resistive load (a resistor). The fact that current and voltage are out of phase means that current is flowing through the inductor when it is not flowing through the load (because the potential across the load is zero). This component of the current only sloshes back and forth in the inductor, and if the inductor has non-zero resistance, it leads to power loss without any energy making it to the load. In this sense, the self-inductance of the transformer leads to potential efficiency loss but it does not preclude the transformer from working. If the resistance of the primary coils can be lowered or the impedance mismatch be compensated for, then these inefficiencies aren't as important. Often there are bigger losses due to magnetic effects if there are iron cores.

This resource gives a good explanation of how self inductance and mutual inductance go together. I don't have time to put it into the answer right now, but I thought you might find it useful.

• what does this lag (out of phase) indicate ? Dec 3, 2014 at 11:43
• I don't mind if people down-vote answers but it is helpful if they indicate why. Dec 3, 2014 at 13:46
• I repeat what significance it has if you say that voltage and current are out of phase ? Dec 3, 2014 at 16:10
• I edited the question to try to address that question. Hopefully that clears it up. Please let me know. Dec 3, 2014 at 17:28

Theo and Scanny have written a beautiful answer, i will try to make it more easier to understand.

The answer lies difference in working of transformer and inductor.

Inductor is an energy storing device whereas transformer is an energy transfer device.

Inductor stores energy in the form of a magnetic field. Transformer transfers electric energy via magnetic domain.

The underlying fact in working of inductor is as iL increases, flux in the core will increase. This implies to facilitate energy storage flux must be present and it should increase with increase with amount of energy we try to deposit.(Here by increase energy means to increase current)

But [transformer is a constant flux device]3, if you increase the load on the transformer, (i.e. secondary current and eventually primary current) the flux in the core does not increase. Flux cancellation takes place due to Lenz law.

So, coming back to your question.

Transformer primary winding has 3 effects,

1. Leakage inductance
2. Magnetizing inductance
3. Self inductance. Self and leakage are very similar by definition since flux is linking to same winding.

1. Self inductance: When secondary of a transformer is open circuited, and LCR meter is connected to primary of transformer winding, meter will show primary winding self inductance. (for more details follow link.)

Here as secondary is open circuited, it is not carrying any current and hence its winding has zero inductance. Hence meter will see only one winding wound on transformer core, that winding will obviously have some inductance (N^2/Reluctance of core).

2. Magnetizing inductance: It is responsible for production of flux in the core in normal working condition. ( Flux /i(magnetizing)). (Note that magnetizing current is constant since magnetizing inductance is in parallel to source.)

Some references suggest that LCR meter should be connected to primary with secondary open. But i dont think it is right since, in that case L1 and Lmag will be in parallel connection. Lmag is generally very large compared to L1, hence LCR will give value closer to L1.

3. Leakage inductance: When LCR meter is connected to primary and secondary is short circuited with large cross sectioned wire. Meter will read leakage inductance.

In normal working as stated earlier, L2 will cancel flux produced by L1 hence, the energy storage property of L1 (primary winding) as inductor will be weakened. (Still primary can store little amount of energy in the leakage inductance. Since leakage flux is only linking with one winding through air.)

Leakage inductance however is an undesirable effect, it will not only reduce voltage gain (transfer ratio) of the transformer but will also produce phase lag in the primary current and voltage. ( Which is very undesirable since power factor of ideal transformer is only governed by load power factor. Lag caused due to leakage will reduce this ideality. )

Once again to address your question primary winding inductance will not ruin the transformer operation since inductance property of transformer winding is very less. ( it is also a desirable property.)

Hope it helps you and rest of the readers.

• Please avoid text with your screenshots. Use mathjax to typeset equations. Jul 15, 2023 at 21:22