Two coils $$C_1$$ and $$C_2$$ are placed close to each other. The magnetic flux $$\phi_2$$ linked with the coil $$\mathrm{C}_2$$ varies with the current $$I_1$$ flowing in coil $$C_1$$, as shown in the figure. Find

(i) the mutual inductance of the arrangement, and

(ii) the rate of change of current $$\left(\frac{d \mathrm{I}_1}{d t}\right)$$ that will induce an emf of 100 V in coil C$$_2$$.

(a) A plane wave-front propagating in a medium of refractive index '$$\mu_1$$' is incident on a plane surface making an angle of incidence (i). It enters into a medium of refractive index $$\mu_2\left(\mu_2>\mu_1\right)$$. Use Huygen's construction of secondary wavelets to trace the retracted wave-front. Hence, verify Snell's law of refraction.

OR

Using Huygen's construction, show how a plane wave is reflected from a surface. Hence, verify the law of reflection.

An alternating voltage of $$220 \mathrm{~V}$$ is applied across a device $$X$$. A current of 0.22 A flows in the circuit and it lags behind the applied voltage in phase by $$\pi / 2$$ radian. When the same voltage is applied across another device $$Y$$, the current in the circuit remains the same and it is in phase with the applied voltage.

(i) Name the devices $$X$$ and $$Y$$ and,

(ii) Calculate the current flowing in the circuit when the same voltage is applied across the series combination of $$\mathrm{X}$$ and $$\mathrm{Y}$$.

State the basic principle behind the working of an ac generator. Briefly describe its working and obtain the expression for the instantaneous value of emf induced.