Question

Magnetic flux in a circuit containing a coil of resistance $2\,\,\Omega$ changes from $2.0 \,Wb$ to $10 \,Wb$ in $0.2 \,s$. The charge passed through the coil in this time is :

• A. 0.8 C
• B. 1.0 C
• C. 5.0 C
• D. 4.0 C

Answer 1

Answer: (D)

From Faradays law of electromagnetic induction,
the emf $(e)$ induced is equal to rate of change of magnetic flux $(\phi )$ ,
i.e., $\left| e \right|=\frac{d\phi }{dt}$
Also, $\left| e \right|=IR$
where $I$ is current and $R$ is resistance.
$\therefore$ $IR=\frac{d\phi }{dt}$
$\Rightarrow$ $I\,dt=\frac{d\phi }{R}$
Charge, $q=Idt=\frac{d\phi }{R}$
Given, $d\phi =10-2=8\,Wb,\,R=2\,\Omega$
$\therefore$ $q=\frac{8}{2}=4\,C$