The magnetic flux through a coil of resistanc | vedclass

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(A) The induced current $i$ is given by Faraday's law: $i = \frac{|e|}{R} = \frac{1}{R} \left| \frac{d\phi}{dt} \right|$.Rearranging this,we get $|d\p

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(A) The induced current $i$ is given by Faraday's law: $i = \frac{|e|}{R} = \frac{1}{R} \left| \frac{d\phi}{dt} ight|$.Rearranging this,we get $|d\phi| = i R \, dt$.The total change in magnetic flux $\Delta \phi$ is the integral of $i R \, dt$ over the time interval:$\Delta \phi = R \int i \, dt$.The integral $\int i \, dt$ represents the area under the $i-t$ graph.From the given graph,the area is a triangle with base $t = 0.1 \, s$ and height $i = 4 \, A$.Area $= \frac{1}{2} 	imes 	ext{base} 	imes 	ext{height} = \frac{1}{2} 	imes 0.1 	imes 4 = 0.2 \, C$.Therefore,the change in flux $\Delta \phi = R 	imes 	ext{Area} = 10 	imes 0.2 = 2 \, Wb$.

The magnetic flux through a coil of resistance $10\,\Omega$ changes. As a result,an induced current is developed in it,which varies with time as shown in the figure. The magnitude of the change in magnetic flux through the coil in webers is:

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