Question

3) Two cylindrical copper wires with a radius of 22 cm are connected to a battery and then they are connected across an incandescent light bulb and the light bulb turns on and is some brightness. If you took the same battery and connected coppers two wires which were a factor of 5 times longer than the first two wires to the same lightbulb so that the lightbulb was the exact same brightness as the first wires (it's not dimmer or brighter), what must be the radius of the second wires in cm?

Answer 1

Given is:-

Initial Radius  

now,

equating both the resistances we get

or

(specific resistance of both the wires will be same)

or

which gives us

by plugging the value of initial radius we get

This is the required radius