# Why is the power unchanged by a transformer?

If we have a step up transformer then the voltage at the secondary side will be more than the voltage at the primary side. Since we all know that

POWER = VOLTAGE * CURRENT

and because voltage at the secondary side is now more than the voltage at the primary side.

So will it not make the power at the secondary side more that the power at the primary side according to the relation P=VI?

Then why is it said that power will remain same at the both side of the transformer when voltage on both sides is not same?

• Hint: The primary and secondary currents are also not equal. – The Photon Nov 27 '19 at 18:45
• Unlike a resistor or capacitor, a transformer forms a coupling between two different circuits. The two "sides" of the transformer are not members of the same circuit the same way that the two terminals of a resistor are. – Ryan Cavanaugh Nov 27 '19 at 21:44

So will it not make the power at the secondary side more that the power

No. A transformer cannot generate power out of thin air and so the power on both sides is (roughly) the same. That means if the voltage on the secondary side is higher then the secondary current is actually lower than the primary.

Let's look at simple example. Let's say you have a light bulb that consumes 100W at 200V. Assuming it's a simple resistor, the light bulb will draw a current of 0.5A and it's resistance is 400 Ohm.

Now we connect the lightbulb to a 100V outlet using a 2:1 step up transformer. On the secondary side all remains the same: we have 200V and consume 100W. On the primary side the voltage is half of the secondary, i.e. 100V but the primary current is double: 1A. So the primary power is also 100W and that's the power that's drawn from the outlet.

A transformer is similar to the transmission of a car. For a transformer: as the voltage goes up, the current goes down. For a transmission: as you go into high gear, the wheels turn faster but there is less force (or torque). Otherwise you could go infinitely fast by going to a higher and higher gear.

You don't seem to be considering the currents in the primary and secondary. If you connect a resistive 'load', for example an old-fashioned filament lamp, across the secondary, there will be a current through it. There will then also be a (larger) current through the primary in a step-up transformer. To a fair approximation, the mean power supplied to the primary will equal the mean power supplied by the secondary.

But why should these mean powers be equal? At high school level it's usual to tell students that it is because transformers can't dissipate much power internally (the resistances of the primary and secondary are small, and the soft iron core, if laminated, won't carry significant eddy currents). Since energy is conserved and not much of the energy put in becomes random thermal energy in the transformer itself, the electrical power out almost equals the electrical power going in.

This explanation isn't wrong, but it leaves a lot of questions unanswered. For example, currents and voltages are alternating (glossed over in the naïve equation $$V_p I_p=V_s I_s$$). And as the resistance of the coils is low, why doesn't the primary take a high current from the supply even when the secondary is open circuit? In a full treatment of transformers the variation of magnetic flux in the core and emfs induced in both coils play a major role. It's fairly intricate, university-level stuff.