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 $