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A $220 \mathrm{~V}$ input is supplied to a transformer. The output circuit draws a current of $2.0 \mathrm{~A}$ at $440 \mathrm{~V}$. If the efficiency of the transformer is $80 \%$, the current drawn by the primary windings of the transformer is
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The correct answer is:
$5.0 \mathrm{~A}$
Efficiency is defined as the ratio of output power and input power
$$
\text { ie, } \begin{aligned}
\eta \% & =\frac{\mathrm{P}_{\text {out }}}{\mathrm{P}_{\text {in }}} \times 100=\frac{\mathrm{V}_s \mathrm{i}_s}{\mathrm{~V}_{\mathrm{p}} \mathrm{i}_{\mathrm{p}}} \times 100 \\
80 & =\frac{2 \times 440}{220 \times \mathrm{i}_{\mathrm{p}}} \times 100 \\
\Rightarrow \quad \mathrm{i}_{\mathrm{p}} & =5 \mathrm{~A}
\end{aligned}
$$
$$
\text { ie, } \begin{aligned}
\eta \% & =\frac{\mathrm{P}_{\text {out }}}{\mathrm{P}_{\text {in }}} \times 100=\frac{\mathrm{V}_s \mathrm{i}_s}{\mathrm{~V}_{\mathrm{p}} \mathrm{i}_{\mathrm{p}}} \times 100 \\
80 & =\frac{2 \times 440}{220 \times \mathrm{i}_{\mathrm{p}}} \times 100 \\
\Rightarrow \quad \mathrm{i}_{\mathrm{p}} & =5 \mathrm{~A}
\end{aligned}
$$
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