Question

Some magnetic flux is changed from a coil of resistance $10\Omega$. As a result, an induced current is developed in it, which varies with time as shown in figure. Find the magnitude of the change in flux through the coil in weber.

Answer 1

We know that, the current can be obtained as:

$i=\frac{1}{R}\frac{d\varphi }{dt}$

$\int iRdt=\int d\varphi$

$R\int \left(idt\right)=\Delta \varphi$

$idt$ = Area under the curve
$\int idt=\frac{1}{2}\times 0.1\times 4=0.2As$
$\Delta \varphi =0.2R=2Wb$