The magnetic flux through a coil of resistanc | vedclass

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(C) According to Faraday's law of electromagnetic induction,the induced electromotive force (emf) is given by $e = \frac{\Delta \phi}{\Delta t}$.Since

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(C) According to Faraday's law of electromagnetic induction,the induced electromotive force (emf) is given by $e = \frac{\Delta \phi}{\Delta t}$.Since the coil has a resistance $R$,the induced current is $i = \frac{e}{R}$,which implies $e = iR$.Equating the two expressions for $e$,we get $iR = \frac{\Delta \phi}{\Delta t}$.Rearranging the terms,we find the change in magnetic flux: $\Delta \phi = R 	imes (i \cdot \Delta t)$.The term $(i \cdot \Delta t)$ represents the area under the current-time $(i-t)$ graph.From the given graph,the area is a right-angled triangle with base $0.1\,s$ and height $4\,A$.Area $= \frac{1}{2} 	imes 	ext{base} 	imes 	ext{height} = \frac{1}{2} 	imes 0.1 	imes 4 = 0.2$.Substituting the values,we get $\Delta \phi = 10 	imes 0.2 = 2\,Wb$.Therefore,the magnitude $\left| \Delta \phi ight| = 2\,Wb$.

The magnetic flux through a coil of resistance $10\,\Omega$ is changed by $\Delta \phi$ in $0.1\,s$. The resulting current in the coil varies with time as shown in the figure. Then,the magnitude $\left| \Delta \phi \right|$ is equal to (in weber):

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