Question

In a coil resistance $100\Omega$, a current is induced by changing the magnetic flux through it as shown in the figure. The magnitude of change in flux through the coil is :

• A. 250 Wb
• B. 275 Wb
• C. 200 Wb
• D. 225 Wb

Answer 1

The correct option is A 250 Wb

$Given:$ R=100$\Omega$

$Solution:$ Induced constant, $I=\frac{e}{R}$

Here, $e=$ induced $emf=\frac{d\varphi }{dt}$

$\begin{array}{cc}I& =\frac{1}{R}=\left(\frac{d\varphi }{dt}\right)\cdot \frac{1}{R}\\ d\varphi & =Rdt\\ \varphi & =\int /Rdt\end{array}$

$\therefore$ Here $R$ is constant

$\therefore$ $\varphi =R\int Idt$

$\begin{array}{cc}\int I\cdot dt& =\text{Area under}I-t\text{graph}\\ & =\frac{1}{2}\times 10\times 0.5=2.5\end{array}$

$\therefore$ $\dot{\varphi }=R\times 2.5=100\times 2.5=250Wb$