Question 21

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 $$|\Delta\phi|$$ is equal to (in weber)

$$i = \frac{\varepsilon}{R} = \frac{1}{R}\left\vert{}\frac{d\phi}{dt}\right\vert{} \implies d\phi = R \cdot i \, dt$$

$$\vert{}\Delta \phi\vert{} = R \int i \, dt = R \times (\text{Area under } i-t \text{ graph})$$

$$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 0.1 \times 4 = 0.2\text{ C}$$

$$\vert{}\Delta \phi\vert{} = 10 \times 0.2 = 2\text{ Wb}$$

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