Why Power remains same in a Transformer?
$$ P_{OUT} = P_{IN} - losses $$

Ignoring the losses:

$$ P_{OUT} = P_{IN}$$
$$ V_{OUT}I_{OUT} = V_{IN}I_{IN}$$

Rearranging:

$$ I_{OUT} = \frac {V_{IN}}{V_{OUT}}I_{IN}$$

So, for a step up transformer where VOUT > VIN the output current is less than the input current by the voltage step-up ratio.



From the comments:


  So if the voltage increases on secondary side then the current shouldnt increase also on secondary side ? doesnt the mathematical expression violates the ohm law in this case ?








simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. Two scenarios.


In (a) the current will be \$ \frac {V}{R} = \frac {120}{120} = 1 \ \text A \$.
In (a) the power in R1 will be \$ P = VI = 120 \times 1 = 120 \ \text W \$.
In (a) the primary current will be 1 A.


If we use the same value resistor for R2 with double the voltage then we have situation (b).


In (b) the current will be \$ \frac {V}{R} = \frac {240}{120} = 2 \ \text A \$.
In (b) the power in R2 will be \$ P = VI = 240 \times 2 = 480 \ \text W \$.
In (b) the primary power will have to be at least 480 W.
In (b) the primary current will have to be \$ I = \frac {P}{V} = \frac {480}{120} = 4 \ \text A \$.


The main thing you need to realise from the answers to your question is that Ohm's law applies to the resistors R1 and R2, and not to the transformers!




  In (b) the primary current will have to be 4 A ? How the primary side will manage to make the primary current high?


Transformers transform voltages and currents but this has the effect of transforming impedances too. 


  impedance
  /ɪmˈpiːd(ə)ns/
  noun,
  the effective resistance of an electric circuit or component to alternating current, arising from the combined effects of ohmic resistance and reactance.


So you can think of an impedance as resistance to AC.

The impedance seen looking into the primary in your step-up transformer will be \$ \frac {1}{n^2}Z_L \$, where n is the voltage step-up ratio. So with R2 = 120 &Omega; the mains supply will see a load of \$ \frac {1}{2^2}120 = 30 \ \Omega \$. Therefore the current will be 4 A.

Note that if R2 is removed and the transformer is open-circuit that no current will be drawn by the primary. (In real transformers there will be a little magnetizing current.)