Question

In a coil of 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. $275Wb$
• B. $200Wb$
• C. $225Wb$
• D. $250Wb$

Answer 1

The correct option is D $250Wb$

Induced emf $E=\frac{d\varphi }{dt}$
$\therefore$ $d\varphi =Edt=iRdt$
$△\varphi =\int iRdt$
From the graph, current is given by
$i=-20t+10$
$△\varphi ={\int }_0^{0.5}(-20t+10)\times dt$
$=\frac{-2000}{2}[t^2{]}_0^{0.5}+1000[t{]}_0^{0.5}$
$=-1000\times 0.25+1000\times 0.5$
$=250Wb$