KCET · Physics · Alternating Current
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
- A \(2.5 \mathrm{~A}\)
- B \(5 \mathrm{~A}\)
- C \(0.25 \mathrm{~A}\)
- D \(0.5 \mathrm{~A}\)
Answer & Solution
Correct Answer
(C) \(0.25 \mathrm{~A}\)
Step-by-step Solution
Detailed explanation
\(\mathrm{V}_{\mathrm{p}}=220 \mathrm{~V}, \mathrm{~V}_{\mathrm{s}}=2200 \mathrm{~V}, \mathrm{I}_{\mathrm{p}}=5 \mathrm{~A}, \mathrm{I}_{\mathrm{s}}=\) ?
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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