In a transformer designed to triple its input voltage, what is the relationship of the turns between the primary and secondary coils?

To determine the relationship between the turns in the primary and secondary coils of a transformer that triples its input voltage, it’s essential to understand the basic principles of transformer operation. The voltage ratio between the primary and secondary coils is directly related to the turns ratio, which is expressed with the formula:

[

\frac{V_s}{V_p} = \frac{N_s}{N_p}

]

Where (V_s) is the secondary voltage, (V_p) is the primary voltage, (N_s) is the number of turns in the secondary coil, and (N_p) is the number of turns in the primary coil.

In the case of a transformer that triples the input voltage, the voltage ratio ( \frac{V_s}{V_p} ) is equal to 3. This means:

[

3 = \frac{N_s}{N_p}

]

To find the relationship between the turns, this can be rearranged to:

[

N_s = 3N_p

]

This means that the secondary winding must have three times as many turns as the primary winding. Conversely, if the primary winding has (N_p) turns, then the secondary must have (3