The Earth is about 24,901 miles around its circumference, or 40,075 kilometers. The movement of electrons through a conductor is not directly measurable without knowing the size of the conductor, at which point the "drift speed" of the electrical current can be measured. However, since conductors are filled with electrons in a state of potential, as soon as the source of electricity is activated, the electrons at the other end of the conductor begin to exit: think of it as a pipe filled with water; as soon as more water is forced into one end, it spills out of the other. This makes the observable speed of electricity about the same as the speed of light: 186,000 miles per second, or 299,792 km/s. With this known a simple calculation gives the speed of electrical activity through a wire stretching around the entire Earth at well under one second, about 0.134 seconds.
The current travels through any conductor at a speed which is same that of speed of light light.This common speed of light and current is 299,792 km/s.
Therefore we can calculate the the time taken by current to travel any distance and light the lights as:
Time taken = (Distance travelled by current)/(Speed of Current)
The diameter of the earth is about 41000 kilometers. Therefor when the wire goes round the earth the current will have to travel this distance before the lights are lighted. thus time taken to light up when wire goes round the earth:
= 41000/299,792 = 0.1368 seconds.
Time to light up when wire goes to sun and back is:
= [Distance of sun from earth) x 2]/speed of current
= 150,000,000/299792 = 500 seconds (approximately)
Distance of Pluto from earth is about 39.3 time distance of sun from earth. There the time taken to light up when the wire goes round the Pluto is:
(39.3*150,000,000*2)/299792 = 19663 seconds
Please note that, as per astronomy, our sun may be considered to be a star. If we do that sun becomes the nearest star. The other nearest star is Proxima Centurai which is about 40 million million kilometers away. The time for lighting up when the wire goes round Proxima Centurai is:
(4*10^13)*2/299792 = 26.69178*10^7 seconds
This is equal to about 8.5 years.
This way we can calculate time taken for lighting up when the wires go around nearest galaxy. The distance of galaxies is in any case measured in term of time taken for light to travel that distance. The galaxy nearest to earth is Large Magellanic Cloud, which is situated 160,000 light years away. There fore the time for lighting up will be twice this number in years, that is 320,000 years.