Question

A wire of resistance 40$\Omega$ is bent into a square. Then consider the following statements:
a) resistance between opposite corners is 20$\Omega$
b) resistance between adjucent corners is 7.5$\Omega$
c) resistance between mid points of opposite sides is 10$\Omega$
d) resistance between mid points of adjacent sides is 15$\Omega$

• A. a and d are correct
• B. b and d are correct
• C. b and c are correct
• D. a and b are correct

Answer 1

The correct option is C b and c are correct

Resistance of a side becomes $10\Omega$
$R_{AC}=\frac{(10+10)(10+10)}{2(10+10)}$$=10\Omega$
$R_{AB}=\frac{10\times 30}{40}=7.5\Omega$
$R_{EG}=\frac{20\times 20}{2\times 20}=10\Omega$
$R_{EH}=\frac{10\times 30}{40}=7.5\Omega$
So, (b) and (c) are correct.