Understanding Transformer Transformation Ratio

The transformation ratio ($K$) of a transformer quantifies the relationship between the voltages and the number of turns in its primary and secondary coils.

Defining the Transformation Ratio

It is defined as the ratio of the number of turns in the secondary coil ($N_s$) to the number of turns in the primary coil ($N_p$):

$K = \frac{N_s}{N_p}$

Alternatively, it can be expressed as the ratio of the secondary voltage ($V_s$) to the primary voltage ($V_p$):

$K = \frac{V_s}{V_p}$

Characteristics of a Step-Up Transformer

A step-up transformer is designed to increase the voltage from the primary side to the secondary side. This implies:

• The voltage in the secondary coil ($V_s$) is greater than the voltage in the primary coil ($V_p$).
• Consequently, the number of turns in the secondary coil ($N_s$) must be greater than the number of turns in the primary coil ($N_p$).

Determining the Transformation Ratio for Step-Up

For a step-up transformer, since $V_s > V_p$ (and $N_s > N_p$), the ratio $K$ will be:

$K = \frac{V_s}{V_p} > 1$

or

$K = \frac{N_s}{N_p} > 1$

Conclusion

Therefore, the transformation ratio ($K$) for a step-up transformer is always greater than 1.

Matching this with the given options, the correct choice is $K > 1$.