Auto-transformer makes effective saving on copper and copper losses, when its transformation ratio is

Copper saving in autotransformer

Consider a 2-winding transformer reconnected as an auto-transformer as shown below:

The turns ratio of an auto-transformer is given by:

where, N₁ = No. of turns of high voltage side

N₂ = No. of turns of low voltage side

The copper used in a transformer is directly proportional to the MMF.

For an ideal auto-transformer: 

The MMF of an auto-transformer is given by:

.........(i)

The MMF of a 2-winding transformer is given by:

 ........(ii)  (By MMF balance equation- )

Dividing equation (i) by (ii), we get:

The percentage saving of copper used in auto-transformer is:

% saving = 

% saving = 

Since the value  is slightly greater than 1.

Therefore, the value of % saving =  is approximately equal to one.