Answer:
As b ∝ (L/r²) and
the distance of the sun from the earth is 0.00001581 light years
and
the distance of the Sirius from the earth is 8.6 light years
hence,
the Sun appear brighter in the sky
Explanation:
The brightness (b) is directly proportional to the Luminosity of the star (L) and inversely proportional to the square of the distance between the star and the observer (r).
thus, mathematically,
b ∝ (L/r²)
now,
given
L for sirius is 23 times more than the sun i.e 23L
now,
the distance of the sun from the earth is 0.00001581 light years
and
the distance of the Sirius from the earth is 8.6 light years
thus,
using the the relation between conclude that the value of brightness for the Sirius comes very very low as compared to the value for brightness for the Sun.
hence, the sun appears brighter
Answer:

is time required to heat to boiling point form initial temperature.
Explanation:
Given:
initial temperature of water, 
time taken to vapourize half a liter of water, 
desity of water, 
So, the givne mass of water, 
enthalpy of vaporization of water, 
specific heat of water, 
Amount of heat required to raise the temperature of given water mass to 100°C:



Now the amount of heat required to vaporize 0.5 kg of water:

where:
mass of water vaporized due to boiling


Now the power rating of the boiler:



Now the time required to heat to boiling point form initial temperature:


The capacitor is used to store electric charge.That is what makes capacitors special. <span>
The charge that flows into the capacitor is stored on the plate of the capacitor that the source voltage is connected to. </span>When current flows into a capacitor, the charges get “stuck” on the plates because they can’t get past the insulating dielectric. One plate is positively charged and the other negatively <span>The stationary charges on these plates create an </span>electric field. <span>When charges group together on a capacitor like this, the cap is storing electric energy just as a battery might store chemical energy.</span>
Considering the unknown resistence as R and using the Ohm's First Law, we have:
The equivalent resistence is given by the resistor series with the lamp resistence.

If you notice any mistake in my english, please let me know, because i am not native.