Q151 / 160 · TS EAMCET 2022 (19 Jul Shift 1) · Physics
A wire loop of area $0.2 \mathrm{~m}^2$ has a resistance of $20 \Omega$. A magnetic field pointing normal to the loop has a magnitude of $0.25 \mathrm{~T}$ and is reduced to zero at a uniform rate in $10^{-4} \mathrm{sec}$. What is induced emf and resulting current?
- A$50 \mathrm{~V}, 2.5 \mathrm{~A}$
- Correct answerB$500 \mathrm{~V}, 25 \mathrm{~A}$
- C$250 \mathrm{~V}, 12.5 \mathrm{~A}$
- D$500 \mathrm{~V}, 2.5 \mathrm{~A}$
Solution
Induced emf is given by
$$
\begin{aligned}
& |\varepsilon|=\left|-\frac{\mathrm{dt}}{\mathrm{dt}}\right|=\left|-\frac{\mathrm{dB} \cdot \mathrm{A}}{\mathrm{dt}}\right| \\
& =\frac{0.25 \times 0.2}{10^{-4}}=500 \mathrm{~V}
\end{aligned}
$$
Current, $I=\frac{V}{R}$
$$
=\frac{500}{20}=25 \mathrm{~A}
$$
Hence, the correct answer is option: 'B'.