Question

The distribution circuit of a residential power line is operated at 2000 V rms. This voltage must be reduced to 240 V rms for use within the residences. If the secondary side of the transformer has 475 turns, how many turns are in the primary?

Answer 1

`N_p\approx3958`

Step-by-step explanation:

In an ideal transformer the relationship between the voltages is proportional to the ratio between the number of turns of the windings. Thus:

`(V_p)/(V_s) =(N_p)/(N_s)`

Where:

`V_p=Voltage\hspace{3}in\hspace{3}primary\hspace{3}coil`

`V_s=Voltage\hspace{3}in\hspace{3}secondary\hspace{3}coil`

`N_p=Turns\hspace{3}on\hspace{3}primary\hspace{3}coil`

`N_s=Turns\hspace{3}on\hspace{3}secondary\hspace{3}coil`

So, solving for
`N_p`

`N_p=N_s*(V_p)/(V_s) =475*(2000)/(240) =3958.333333\approx3958`