In a certain place, the horizontal component of magnetic field is $\frac{1}{\sqrt{3}}$ times to vertical component. The angle of dip at this place is

• zero

• $\mathrm{\pi }/3$

• $\mathrm{\pi }/2$

• $\mathrm{\pi }/6$

An alternating voltage e = 200 sin 100 t is applied to a series combination R = 30 Ω and an inductor of 400 mH. The power factor of the circuit is

• 0.01

• 0.2

• 0.6

• 0.042

The flux linked with a circuit is given by $\mathrm{\varphi } = {\mathrm{t}}^3 + 3\mathrm{t} - 7$.The graph between time (x-axis) and induced emf (y-axis) will be a

• straight line through the origin

• straight line with positive intercept

• parabola not through the origin

• parabola through the origin

If the self-inductance of 500 tum coil is 125 mH, then the self inductance of similar coil of 800 turns is

• 48.8 mH

• 200 mH

• 187.5 mH

• 320 mH

A resistor 30 Ω, inductor of reactance 10 Ω and capacitor of reactance 10 Ω are connected in series to an AC voltage source $\mathrm{e} = 300\sqrt{2} \sin \left(\mathrm{\omega t}\right)$. The current in the circuit is

• $10\sqrt{2} \mathrm{A}$

• 10 A

• $30\sqrt{11} \mathrm{A}$

• $30/ \sqrt{11} \mathrm{A}$

A plane electromagnetic wave travelling along the X- direction has a wavelength of 3 mm. The variation in the electric field occurs in the Y-direction with an amplitude 66 Vm^-1. The equations for the electric and magnetic fields as a function of x and t are respectively.

• $$\begin{gathered} {\mathrm{E}}_{\mathrm{y}} = 33 \cos \mathrm{\pi } \times {10}^{11} \left(\mathrm{t} - \frac{\mathrm{x}}{\mathrm{c}}\right) \\ {\mathrm{B}}_{\mathrm{z}} = 1.1 \times {10}^{-7} \cos \mathrm{\pi } \times {10}^{11} \left(\mathrm{t} - \frac{\mathrm{x}}{\mathrm{c}}\right) \end{gathered}$$

• $$\begin{gathered} {\mathrm{E}}_{\mathrm{y}} = 11 \cos 2\mathrm{\pi } \times {10}^{11} \left(\mathrm{t} - \frac{\mathrm{x}}{\mathrm{c}}\right) \\ {\mathrm{B}}_{\mathrm{y}} = 11 \times {10}^{-7} \cos 2\mathrm{\pi } \times {10}^{11} \left(\mathrm{t} - \frac{\mathrm{x}}{\mathrm{c}}\right) \end{gathered}$$

• $$\begin{gathered} {\mathrm{E}}_{\mathrm{x}} = 33 \cos \mathrm{\pi } \times {10}^{11} \left(\mathrm{t} - \frac{\mathrm{x}}{\mathrm{c}}\right) \\ {\mathrm{B}}_{\mathrm{x}} = 11 \times {10}^{-7} \cos \mathrm{\pi } \times {10}^{11} \left(\mathrm{t} - \frac{\mathrm{x}}{\mathrm{c}}\right) \end{gathered}$$

• $$\begin{gathered} {\mathrm{E}}_{\mathrm{y}} = 66 \cos 2\mathrm{\pi } \times {10}^{11} \left(\mathrm{t} - \frac{\mathrm{x}}{\mathrm{c}}\right) \\ {\mathrm{B}}_{\mathrm{z}} = 2.2 \times {10}^{-7} \cos 2\mathrm{\pi } \times {10}^{11} \left(\mathrm{t} - \frac{\mathrm{x}}{\mathrm{c}}\right) \end{gathered}$$

A plane electromagnetic wave travels in free space along x-axis. At a particular point in space, the electric field along y-axis is 9.3 Vm^-1. The magnetic induction is

• 3.1 × 10^-8 T

• 3 × 10^-5 T

• 3 × 10^-6 T

• 9.3 × 10^-6 T

If the ratio of amounts of scattering of two light waves is 1 :4, the ratio of their wavelengths is

• 1 : 2

• $\sqrt{2} : 1$

• $1 : \sqrt{2}$

• 1 : 1

59.

In Young's experiment, the third bright band for light of wavelength 6000 $\stackrel{\circ }{\mathrm{A}}$ coincides with the fourth bright band for another source of light in the same arrangement. Then the wavelength of second source is

• $3600 \stackrel{\circ }{\mathrm{A}}$

• $4000 \stackrel{\circ }{\mathrm{A}}$

• $5000 \stackrel{\circ }{\mathrm{A}}$

• $4500 \stackrel{\circ }{\mathrm{A}}$

If the angle of minimum deviation is of 60° for an equilateral prism, then the refractive index of the material of the prism is

• 1.41 

• 1.5

• 1.73

• 1.33