The transformer equation:

$\overline{)\frac{{\mathbf{V}}_{\mathbf{p}}}{{\mathbf{V}}_{\mathbf{s}}}{\mathbf{=}}\frac{{\mathbf{I}}_{\mathbf{s}}}{{\mathbf{I}}_{\mathbf{p}}}{\mathbf{=}}\frac{{\mathbf{N}}_{\mathbf{p}}}{{\mathbf{N}}_{\mathbf{s}}}}$

Relating voltage and the number of turns, then solving for V_{s}:

$\overline{){{\mathbf{V}}}_{{\mathbf{s}}}{\mathbf{=}}\frac{{\mathbf{V}}_{\mathbf{p}}{\mathbf{N}}_{\mathbf{s}}}{{\mathbf{N}}_{\mathbf{p}}}}$

The rms secondary voltage is:

$\overline{){{\mathbf{V}}}_{{\mathbf{s}}}{\mathbf{\left(}}{\mathbf{rms}}{\mathbf{\right)}}{\mathbf{=}}\frac{{\mathbf{V}}_{\mathbf{p}}{\mathbf{N}}_{\mathbf{s}}}{\sqrt{\mathbf{2}}{\mathbf{N}}_{\mathbf{p}}}}$

**#1**

${{\mathbf{V}}}_{{\mathbf{s}}}{\mathbf{\left(}}{\mathbf{rms}}{\mathbf{\right)}}{\mathbf{=}}\frac{\mathbf{\left(}\mathbf{240}\mathbf{\right)}\mathbf{\left(}\mathbf{2000}\mathbf{\right)}}{\sqrt{\mathbf{2}}\mathbf{\left(}\mathbf{1000}\mathbf{\right)}}$

v_{s}(rms) = 339.4 V

Rank the transformers on the basis of their rms secondary voltage. Rank from largest to smallest. To rank items as equivalent, overlap them.

**#1**

*V*p=240V*N*p=1000turns*N*s=2000turns

**#2**

*V*p=480V*N*p=4000turns*N*s=2000turns

**#3**

*V*p=480V*N*p=2000turns*N*s=1000turns

**#4**

*V*p=120V*N*p=500turns*N*s=2000turns

**#5**

*V*p=240V*N*p=1000turns*N*s=500turns

100 A of rms current is incident on the primary side of each transformer.

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