# Ohm's Law in Transformers: Voltage vs. Current

• waqarrashid33
In summary: The voltage and current in a transformer are related by the turns ratio, not by the resistance of the windings. If the voltage and current are not related according to the turns ratio, then the transformer is not "ideal" and Ohm's Law applies to the deviations from the ideal. The ideal transformer is a mathematical construct that is useful when analyzing a circuit. It is not a physical device.In summary, Ohm's Law states that the current through a conductor is directly proportional to the voltage and inversely proportional to the resistance. This applies to most components, including transformers, but there are some exceptions such as diodes where the resistance may vary with voltage. In a transformer,
waqarrashid33
In transformer when voltage increases on secondry coil then current decreases but i am confuse here that how ohm law is obeyed here.
as
V is d.proportiona to Current.

You are not applying ohms law correctly. In a transformer power in = power out (neglecting inefficiencies). Power being voltage * current. If you adjust the turns ratio for instance to multiply the input voltage by 2 to get 20 volts out the secondary and put a load on the secondary that gives a secondary current of 1 amp, then the input voltage and current would have to be 10 volts at 2 amps. The primary appears to be a 5 ohm load to the generator that is driving it but the power delivered by the generator is still 20 watts. The load on the output of the secondary is in fact 20 ohms, and it would be absorbing 20 watts.

I know about the power i am failed in managing this that how ohm law is working here.

Many components,including transformers,do not obey Ohms law.Ohms law applies only to things like metal conductors and even these deviate from Ohms law when quantities such as temperature change.

There are no exceptions to Ohm's Law. If the resistance of something changes due to temperature, then Ohm's Law applies to the new resistance.

In the above example, a 10 volt to 20 volt transformer has a 20 ohm load on the 20 volt side.

The 20 volts across a 20 ohm load produces a current of 1 amp. All according to Ohm's Law.

The primary of the transformer looks like a 5 ohm resistor to the power supply due to the impedance varying as the square of the turns ratio.

The 10 volt power supply delivers 2 amps into this 5 ohm load, again, according to Ohm's Law.

Notice that the power in equals the power out, since there are no losses.
20 volts times 1 amp = 20 watts. 10 volts times 2 amps = 20 watts.

vk6kro said:
There are no exceptions to Ohm's Law. If the resistance of something changes due to temperature, then Ohm's Law applies to the new resistance.

In the above example, a 10 volt to 20 volt transformer has a 20 ohm load on the 20 volt side.

The 20 volts across a 20 ohm load produces a current of 1 amp. All according to Ohm's Law.

The primary of the transformer looks like a 5 ohm resistor to the power supply due to the impedance varying as the square of the turns ratio.

The 10 volt power supply delivers 2 amps into this 5 ohm load, again, according to Ohm's Law.

So you say if there is no load on the 20 volt side, there will be no current on the 10 volt side. I have to disagree.

Upisoft said:
So you say if there is no load on the 20 volt side, there will be no current on the 10 volt side. I have to disagree.

Why do you disagree?

This is an ideal transformer, so, no, there won't be any current in the primary.

Materials or electrical components which obey Ohms law have,by definition, a single value of resistance regardless of the p.d. applied across them or the current flowing through them.Such components/materials are known as Ohmic components/materials.Mathematically,Ohms law can be expressed by writing that V and I are directly proportional with R,the resistance,being a constant of proportionality.As I said above very few components,including transformers obey Ohms law.If resistance changes then by definition the component deviates from Ohmic behaviour. Resistors and most metals have a resistivity that varies only "slightly" over a wide range of conditions and from a practical viewpoint and depending on their application these are regarded as being Ohmic.
As far as transformers are concerned the wires from which the turns are made can be considered as being Ohmic but the device,as a whole, is certainly not Ohmic.With an ideal transformer the power input=power output(Vp*Ip)=(Vs*Is)
Vp= primary volts
Ip= primary amps
Vs=secondary volts
Is= secondary amps

This is the definition of Ohm's Law in Wikipedia:

Ohm's law states that the current through a conductor between two points is directly proportional to the potential difference or voltage across the two points, and inversely proportional to the resistance between them.

Nothing in there about the resistance staying constant. You can make up your own definition, but don't call it Ohm's Law.

It is very common in electronics for a small change in voltage to be producing a small change in current. Where this happens on a curve, (of V vs I ), will decide what the result is. But even for a small variation, Ohms Law still applies. In the extreme case, the resistance at a point is the slope of the tangent at that point.

With a transformer, Ohm's Law applies at each winding. In any circuit, you can't expect to relate voltages and currents that are not connected to each other.
Even with an imperfect real transformer, Ohm's Law still applies to the various losses and reactive currents inside the transformer.

Go back to your Wiki article and have another look.You will see that the quote you provided is further clarified one addition being:
"More specifically Ohm's law states that R in this relation is constant independant of the current"
Perhaps you should also read on further especially to the sections entitled "linear approximations" and "temperature effects"

That is an application of Ohm's Law, not the Law itself.

Of course, if the voltage and current are directly proportional, then the resistance could not have changed. If it does change, then the voltage and current are related according to the new resistance.

Further down, the author states:
However, in some diode applications, the AC signal applied to the device is small and it is possible to analyze the circuit in terms of the dynamic, small-signal, or incremental resistance, defined as the one over the slope of the V–I curve at the average value (DC operating point) of the voltage (that is, one over the derivative of current with respect to voltage). For sufficiently small signals, the dynamic resistance allows the Ohm's law small signal resistance to be calculated as approximately one over the slope of a line drawn tangentially to the V-I curve at the DC operating point.

So, you can get a large signal or DC voltage, but if you try to vary the current by changing the voltage over a small range, it may take a totally different ratio of voltage to current to do this.
This is still Ohm's Law and it shows the power and beauty of the Law that it can be adapted to situations that Mr Ohm could not have dreamt of.

If you read further down, regarding reactive components, you can see the application of Ohms Law to AC circuits where there may not even be any resistance.

I'm not sure about the point you are making with your first sentence above since I was referring to the definition that you yourself quoted and I pointed out that this omitted information that is relevant to this discussion.
I agree with your second sentence and I agree also that the law can be applied succesfully to other "situations".I am not disputing the power and flexibility of Ohms law so I have a feeling we are at cross purposes here.My main point is that many components do not obey Ohms law and those that do are defined as being "Ohmic conductors" whose resistance remains constant over a wide range of voltages and currents.Since resistivity usually does change with quantities like temperature(all be it often by very small amounts)then Ohmic conductors are useful approximations only.For many,if not most practical problems,any deviations from Ohmic behaviour can be considered as negligible.

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An application of the Law is when you make assumptions that apply in particular cases.

We often assume that large resistors dissipate heat sufficiently well that their resistance does not change much during the course of an experiment.
That does not mean that Ohms Law does not apply in other cases, although some Physics texts would have you believe otherwise.

The change in resistance of components has nothing to do with Ohm's Law.
Whatever the resistance is determines the current that will flow for a given voltage.

If the resistance changes, the calculation becomes different, but you still use Ohm's Law to do it.

And you can't claim Ohm's Law doesn't apply to transformers when it clearly does.

Ohms law can be displayed mathematically by V=IR but the equation,on its own,is not a full expression of the law.Your Wiki definition referred to a constant R,the hyperphysics site definition refers to Ohmic(constantV/I) conductors,the ancient textbook I have just dug out and have in front of me states Ohms law as follows."Under constant physical conditions,the resistance V/I is a constant independent of V and I"(Nelkon and Parker A level physics 4th edition).Even my Concise Collins Dictionary refers to the resistance as being the "constant of proportionality"
V=IR is a powerful equation and the fact that you can use it is not in dispute here but consider the following question:
Given the dimensions of a particular piece of copper wire ,the pd(V) across that wire and the current(I) through the wire find: 1.The resistance (R) of the wire.
2.The resistivity(rho)of copper
3.Check your answer to question 2. by looking up the resistivity of copper in a data book.
A student may use the equation to find the answers to 1. and 2.and feel fairly confident about the answers but then get baffled when they use the data book.The book will refer to other conditions such as temperature coefficient of resistance.In other words there is not a single value for resistivity since this depends on other quantities such as temperature.The equation on its own yields a single value for resistivity only,it is useful equation but it is limited and to give a full description of his answer the student would have to refer to the temperature of the wire under the conditions of the experiment.This limitation applies to the equation only,not to the law which is more powerful than just the equation because when expressed in full it refers to "constant conditions"
As for the transformer,read again what I wrote in post 9

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vk6kro said:
This is an ideal transformer, so, no, there won't be any current in the primary.

There will be current with phase lagging 90 degrees (assuming sine wave AC). With DC there will be the current defined by the resistance of the wire, assuming there was enough time so the current in primary coil has settled.

In ideal transformer will not have magnetizing current. An ideal transformer is considered to have infinite inductance on all windings. So, no current will flow.

$$v = L\frac{di}{dt}$$

No current is equivalent to any constant current. Why there will be no current and not just any constant current?

Huh?

## 1. What is Ohm's Law in transformers?

Ohm's Law in transformers states that the voltage and current in a transformer are inversely proportional to each other. This means that as the voltage increases, the current decreases, and vice versa.

## 2. How does Ohm's Law apply to transformers?

In transformers, Ohm's Law applies to the relationship between the primary and secondary coils. The ratio between the number of turns in each coil determines the voltage and current in the transformer.

## 3. What is the significance of Ohm's Law in transformers?

Ohm's Law is crucial in understanding the behavior of transformers and designing them for different applications. It helps in calculating the voltage and current in a transformer and ensuring that it operates within safe limits.

## 4. Is Ohm's Law always applicable in transformers?

Yes, Ohm's Law is always applicable in transformers as long as the transformer is operating within its rated parameters. If the transformer is overloaded or malfunctioning, Ohm's Law may not apply.

## 5. How is Ohm's Law used to troubleshoot transformer issues?

Ohm's Law can be used to troubleshoot transformer issues by measuring the voltage and current in the primary and secondary coils. If the measured values do not follow the expected relationship based on the turns ratio, it can indicate a problem with the transformer.

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