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