Question

A coil of resistance $400\Omega$ is placed in a magnetic field. If the magnetic flux $\varphi$ $\left(Wb\right)$ linked with the coil varies with time $t$ (sec) as $\varphi =50t^2+4$, the current in the coil at $t=2sec$ is

• A. $0.5A$
• B. $0.1A$
• C. $2A$
• D. $1A$

Answer 1

The correct option is A $0.5A$

Here, $\varphi =50t^2+4Wb,R=400\Omega$
Induced emf, $e=-\frac{d\varphi }{dt}=-\frac{d(50t^2+4)}{dt}=-100tV$

At $t=2s,e=-200V$
On taking magnitude of voltage
$\left(e\right|=200V$,
Induced current in the coil at $t=2\sec$
$I=\frac{\left(}{e}=\frac{200V}{400\Omega }=0.5A$