Q132 / 200 · NEET 2012 (Screening) · Physics
A coil of resistance $400 \Omega$ is placed in a magnetic field. If the magnetic flux $\phi(\mathrm{Wb})$ linked with the coil varies with time $t$ (sec) as $\phi=50 t^2+4$
The current in the coil at $t=2 \mathrm{~s}$ is
- Correct answerA$0.5 \mathrm{~A}$
- B$0.1 \mathrm{~A}$
- C$2 \mathrm{~A}$
- D$1 \mathrm{~A}$
Solution
Induced emf of coil $E=\left|-\frac{d \phi}{d t}\right|_t$ Given, $\phi=50 t^2+4$ and $R=400 \Omega$
$\begin{aligned}
E & =\left|-\frac{d \phi}{d t}\right|_{t=2} \\
& =|100 t|_{t=2}=200 \mathrm{~V}
\end{aligned}$
Current in the coil
$\begin{aligned}
i & =\frac{E}{R}=\frac{200}{400} \\
& =\frac{1}{2}=0.5 \mathrm{~A}
\end{aligned}$
Hence, the correct answer is option: 'A'.