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
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.
$$250\,Wb$$
B.
$$275\,Wb$$
C.
$$200\,Wb$$
D.
$$225\,Wb$$
Answer :
$$250\,Wb$$
Solution :
According to Faraday's law of electromagnetic induction, $$\varepsilon = \frac{{d\phi }}{{dt}}$$
$$\eqalign{ & {\text{Also,}}\,\varepsilon = iR \cr & \therefore iR = \frac{{d\phi }}{{dt}} \Rightarrow \int d \phi = R\int i dt \cr} $$
Magnitude of change in flux $$\left( {{\text{d}}\phi } \right) = R \times $$ area under current vs time graph
$${\text{or,}}\,d\phi = 100 \times \frac{1}{2} \times \frac{1}{2} \times 10 = 250Wb$$
According to Faraday's law of electromagnetic induction, $$\varepsilon = \frac{{d\phi }}{{dt}}$$
$$\eqalign{ & {\text{Also,}}\,\varepsilon = iR \cr & \therefore iR = \frac{{d\phi }}{{dt}} \Rightarrow \int d \phi = R\int i dt \cr} $$
Magnitude of change in flux $$\left( {{\text{d}}\phi } \right) = R \times $$ area under current vs time graph
$${\text{or,}}\,d\phi = 100 \times \frac{1}{2} \times \frac{1}{2} \times 10 = 250Wb$$
