Two capacitors are identical, except that one is empty and the other is fi lled with a dielectric (k 5 4.50). The empty capacitor is connected to a 12.0-V battery. What must be the potential diff erence across the plates of the capacitor fi lled with a dielectric so that it stores the same amount of electrical energy as the empty capacitor?

5.66 V

Explanation:

We know that the electrical energy stored by a capacitor W = 1/2CV² where C = capacitance and V = voltage applied.

Let C₁, C₂ and V₁, V₂  be the capacitances and voltages applied to the empty capacitor and that with dielectric respectively, then for the same electrical energy to be stored in both capacitors,

1/2C₁V₁² = 1/2C₂V₂²

So, V₂ = *(√C₁/C₂)V₁  Since C₂ = kC₁

V₂ = 1/√kV₁ = 1/√4.5 × 12 V = 5.66 V

scattering of light by tiny particles in air to produce the colors we see on sky, is dependent on the following factors:

(i) wavelength of light

(ii) size of the scattering particle  

(iii) distance traveled by light through the atmosphere.

according to rayleigh's law of scattering, the amount of scattering is inversely proportional to the fourth power of its wavelength. shorter the wavelength, greater is its scattering. hence violet/blue light is scattered more than red.

sun's light is a composite light ( visible light) with wavelengths in the range 400 nm (violet) to 700 nm (red). as sunlight passes through our atmosphere, the molecules of air scatter light according to their wavelengths. during sunrise and sunset, the sun's position is below the horizon. hence light from the sun travels a greater distance in the atmosphere when compared to its position a noon.

as sunlight enters the earth's atmosphere, blue light is scattered away and at the end of its journey in the sky, only red and orange wavelengths remain in the beam.

hence at sunrise and sunset, the sky appears reddish orange.