Question

$A B C D$ is a square (see figure) where each side is a uniform wire of resistance $1 \,\Omega$. A point $E$ lies on $C D$ such that if a uniform wire of resistance $1\, \Omega$ is connected across $A E$ and constant potential difference is applied across $A$ and $C$, then $B$ and $E$ are equipotential.

• A. $\frac{C E}{E D}=1$
• B. $\frac{C E}{E D}=\frac{1}{\sqrt{2}}$
• C. $\frac{C E}{E D}=\frac{1}{2}$
• D. $\frac{C E}{E D}=\sqrt{2}$

Answer 1

Answer: (D)

Equivalent resistance between $A$ and $E$ is
$y=\frac{x+1}{x+2}$

For $B$ and $E$ to be equipotent, we get
$\frac{R_{A E}}{R_{A B}}=\frac{R_{E C}}{R_{B C}}$
or $\frac{x+1}{(x+2) \times 1}=\frac{1-x}{1}$
Solve to get $x = \sqrt{2}-1 \Omega$
Now $\frac{C E}{E D}=\frac{1-x}{x}=\sqrt{2} \Omega$