Question

A wire of uniform cross section having resistance 8 0 is bent to form a square ABCD. End A is connected to a point P on the side DC by a wire AP of resistance 1 Q. When V potential difference is applied between A and C, the resistance of part DP if the points B and P are to be at same potential​

Answer 1

Answer:

given = A wire of uniform cross section having resistance 8 0 is bent to form a square ABCD.

to find = effective resistance

solution=

let the effective resistance will be XΩwhich is between CP points so , (1-x)

AP= effective resistance .....( points B and P will be equipotential )

CP=  effective resistance .....( points B and P will be equipotential )

AP=CP

i.e. =   (1 +X)X1 / (1 + X)+1= (1-X)

total resistnce 8Ω .......(given in question)

AB = BC = CD = AD = 2Ω

(1 +X)  = (1-X) X (2+X)

1+X = 2+X-2X X2

X²+2X-1= 0

X= (√2-1)

the effective resistance is X= (√2-1)