A coil of resistance $250 \Omega$ is placed in a magnetic field. If the magnetic flux ( $\phi$ ) linked with…
A coil of resistance $250 \Omega$ is placed in a magnetic field. If the magnetic flux ( $\phi$ ) linked with the coil varies with time t (s) as $\phi=50 \mathrm{t}^2+7$. The current in the coil at $t=4 \mathrm{~s}$ is
1.3 A
1.4 A
$\quad 1.5 \mathrm{~A}$
$\quad 1.6 \mathrm{~A}$
Solution
Induced e.m.f. is given as $|e|=\frac{d \phi}{d t}$ Given, $\phi=50 \mathrm{t}^2+7$
$\therefore \quad|e|=\frac{d}{d t}\left(50 t^2+7\right)=100 t$ For $\mathrm{t}=4 \mathrm{~s}$, $e=100(4)=400 \mathrm{~V}$
Current, $I=\frac{V}{R}=\frac{400}{250}=1.6 \mathrm{~A}$