Question

A resistance of 2 ohm is connected across 1 shape of a metre bridge and an unknown resistance greater than 2 ohm is connected across the other gap when this resistance are interchanged the balance point shift by 20 cm neglecting any correction the unknown resistance is

Answer 1

Known resistance , R = 2 ohm
Let unknown resistance  be X 
let the balance point for the connection be  l 
so , 
 R/X  =  l / 100-l 
 2/X  = l / 100-l  .....................eq 1 

when they are interchanged ,(note: as it is given that unknown resistance is greater than the known resistance , so , balance point will shift toward more side or balance point will increase its value)

X/2 = l + 20/100-20-l  =  l + 20 / 80-l  ..........................eq 2 

multiplying eq 1 and 2

2/X  x  X/2  =  (l/100-l) x (l+20/80-l)
⇒ 1  = (l² + 20 l)/(8000 - 100l - 80l + l²)
⇒l² - 180l + 8000 = l² + 20l
⇒200l =  8000 
⇒ l  = 8000/200 = 40 cm 

hence , original balance point(before interchanging ) is 40 cm 
put this value in eq 1
2/X = 40/60 
⇒ X = (60/40)x2 = (3/2)x2 = 3 ohm

hence , the unknown resistance is now known with the value of 3 ohm.......................................................................................................

hope , you got this 
if not , ask me any time 


MARK AS BRAINLIEST