Why the number of primary turns of coil and secondary turns of coil are not made equal?

Explanation:

Since, the transformer would not change the voltage as the ratio of primary to secondary turns is proportional to the ratio of primary to secondary voltage. There may be instances of the isolation transformers or line conditioners where you could use the two coils to as a buffer to cut down noise, but without a ratio that fits your needs the non transforming transformer will just lose power at the coils.

where are the vectors ?

where is the circuit diagram ?