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A current of $5 \mathrm{~A}$ is flowing at $220 \mathrm{~V}$ in the primary coil of a transformer. If the voltage produced in the secondary coil is $2200 \mathrm{~V}$ and $50 \%$ of power is lost, then the current in secondary will be
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Verified Answer
The correct answer is:
$0.25 \mathrm{~A}$
$\mathrm{V}_{\mathrm{p}}=220 \mathrm{~V}, \mathrm{~V}_{\mathrm{s}}=2200 \mathrm{~V}, \mathrm{I}_{\mathrm{p}}=5 \mathrm{~A}, \mathrm{I}_{\mathrm{s}}=$ ?
Power loss $=50 \%$
Efficiency of transformer ( $\eta$ ) is defined as the ratio of output power and input power
$$
\eta \%=\frac{\mathrm{P}_{\mathrm{out}}}{\mathrm{P}_{\mathrm{in}}} \times 100=\frac{\mathrm{V}_{\mathrm{s}} \mathrm{I}_{\mathrm{s}}}{\mathrm{V}_{\mathrm{p}} \mathrm{I}_{\mathrm{p}}} \times 100
$$
$$
\begin{aligned}
50 &=\frac{2200 \times \mathrm{I}_{\mathrm{s}}}{220 \times 5} \times 100 \\
\mathrm{I}_{\mathrm{s}} &=0.25 \mathrm{~A}
\end{aligned}
$$
Power loss $=50 \%$
Efficiency of transformer ( $\eta$ ) is defined as the ratio of output power and input power
$$
\eta \%=\frac{\mathrm{P}_{\mathrm{out}}}{\mathrm{P}_{\mathrm{in}}} \times 100=\frac{\mathrm{V}_{\mathrm{s}} \mathrm{I}_{\mathrm{s}}}{\mathrm{V}_{\mathrm{p}} \mathrm{I}_{\mathrm{p}}} \times 100
$$
$$
\begin{aligned}
50 &=\frac{2200 \times \mathrm{I}_{\mathrm{s}}}{220 \times 5} \times 100 \\
\mathrm{I}_{\mathrm{s}} &=0.25 \mathrm{~A}
\end{aligned}
$$
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