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\mathrm{A B C D} is a square of side 'a' metres and is made of wires of resistance \mathrm{x} ohms/metre. Similar wires are connected acroos the diagonals \mathrm{AC \& BD}. The effective resistance between the corners \mathrm{A \& C} will be

Option: 1

\mathrm{(2-\sqrt{ } 2) a x}


Option: 2

\mathrm{6 a x}


Option: 3

\mathrm{3ax}


Option: 4

\mathrm{(3-\sqrt{ } 2) a x}


Answers (1)

best_answer



\mathrm{ \frac{1}{R}=\frac{1}{2 a x}+\frac{1}{2 a x}+\frac{1}{\sqrt{2} a x}=\frac{1}{a x}\left(1+\frac{1}{\sqrt{2}}\right)=\frac{1}{a x}\left(\frac{\sqrt{2}+1}{\sqrt{2}}\right) }
\mathrm{ R=\frac{a x \sqrt{2}}{\sqrt{2}+1}=a x \sqrt{ } 2(\sqrt{ } 2-1) \\ R=a x(2-\sqrt{ } 2) }

\mathrm{ \therefore (A )}

Posted by

Suraj Bhandari

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