A power transmission line feeds input power

Question:

A power transmission line feeds input power at $2300 \mathrm{~V}$ to a step down transformer with its primary windings having 4000 turns. The output power is delivered at $230 \mathrm{~V}$ by the transformer. If the current in the primary of the transformer is $5 \mathrm{~A}$ and its efficiency is $90 \%$, the output current would be:

  1. (1) $50 \mathrm{~A}$

  2. (2) $45 \mathrm{~A}$

  3. (3) $35 \mathrm{~A}$

  4. (4) $25 \mathrm{~A}$


Correct Option: , 2

Solution:

(2) Efficiency, $\eta=\frac{P_{\text {out }}}{P_{\text {in }}}=\frac{V_{s} I_{s}}{V_{p} I_{p}}$

$\Rightarrow 0.9=\frac{230 \times \mathrm{I}_{\mathrm{S}}}{2300 \times 5}$

$\Rightarrow \mathrm{I}_{\mathrm{s}}=0.9 \times 50=45 \mathrm{~A}$

Output current $=45 \mathrm{~A}$

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