1. A series RC circuit has a time constant of 1.0 s. The battery has a voltage of 50 V and the maximum current just after closing the switch is 500 mA. The capacitor is initially uncharged. What is the charge on the capacitor 2.0 s after the switch is closed?

The unit of charge is Coulomb.

The charge on the capacitor after 2 second is 0.43 Coulomb.

To finding the voltage while charging a capacitor is given as,

Here , V₀ is the initial potential, R is the resistance and C is the capacitance

It is given that V₀ = 50 V and maximum current I is given as 500 mA.

So,  

Time constant = RC = 1

 So,    

Now, we have  V₀ = 50 V, R = 100 Ω, C = 1/100 F and t = 2 s.

We know that,  

Thus, the charge on the capacitor after 2 s is 0.43 C.

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The charge on the capacitor after 2 s is 0.43 C.

Explanation:

The formula for finding the voltage while charging a capacitor is

Here , V₀ is the initial potential before charging and t is the time at which we have to determine the voltage, R is the resistance and C is the capacitance for the given circuit.

The given problem have given us the values for V₀ = 50 V and maximum current I is given as 500 mA.

Then, resistance can be determined using Ohm's law:

The capacitance is defined as the ratio of charge to the unit voltage.

Here T is the time constant which is given as 1 s and R is found to be 100 ohm, then capacitance will be

So, the values for parameters like V₀ = 50 V, R = 100 Ω, C = 10 mF and t = 2 s.

Then,

V= 43 V.

Then,

Thus, the charge on the capacitor after 2 s is 0.43 C.

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.

jupiter is the largest planet in our solar system, having a mass and radius that are respectively, 318 and 11.2 times that of earth. suppose that an object falls from rest near the surface of each planet and that the acceleration due to gravity remains constant during the fall. each object falls the same distance before striking the ground. determine the ratio of the time of fall on jupiter to that on earth.