Question

Magnetic flux changes through a coil of resistance $10\Omega .$ As a result, an induced current is developed in it, which varies with time as shown. The magnitude of change in magnetic flux through the coil is


$[$0.77 Mark$]$

• A. $1.5\text{Wb}$
• B. $3.5\text{Wb}$
• C. $2.5\text{Wb}$
• D. $6.1\text{Wb}$

Answer 1

The correct option is C $2.5\text{Wb}$

As we know that
$E=-\frac{d\varphi }{dt}$

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

$\Rightarrow \left|\begin{array}{c}d\varphi \end{array}\right|=idtR$

$\Rightarrow \left|\begin{array}{c}\varphi \end{array}\right|=R\int idt$

The value of $\int idt$ is given by the area under the $i$ - $t$ graph.

$\Rightarrow \left|\begin{array}{c}\varphi \end{array}\right|=R\int idt=10\times \frac{1}{2}\times 5\times 0.1$

$=2.5\text{Wb}$