Question

a wire of resistance 20 ohms is bent to form a closed square. What is the resistance across a diognal of the square?

Answer 1

If the wire is bent to form a square,then the resistance of the side of the square=20/4=5
Across the diagonal,
first calculate the resistance through the two sides that is
R1=5+5=10
then through the diagonal,R2=root over of(5^2+5^2)=5*root2
as R1 and R2 are parallel to each other,
1/R=1/R1+1/R2
1/R=1/10+1/5*root2
1/R=(root2+root2)/10*root2
1/R=2*root2/10*root2
root2 cancelled in both,hence
1/R=2/10
1/R=1/5
R=5
Hope it helped you.