# A wire of resistance $R$ is bent to form a square $ABCD$ as shown in the figure. The effective resistance between $E$ and $C$ is :($E$  is mid-point of arm CD) Option 1) $R$ Option 2)  $\frac{7}{64}R$ Option 3) $\frac{3}{4}R$ Option 4) $\frac{1}{16}R$

distribution of Resistance (R) in square $ABCD$

$\Rightarrow \frac{1}{Req}=\frac{1}{R/8}+\frac{1}{7R/8}$

$\Rightarrow \frac{8}{R}+\frac{8}{7R}$

$=\frac{56+8}{7R}$

$=\frac{64}{7R}$

$Req=\frac{7R}{64}$

Option 1)

$R$

Option 2)

$\frac{7}{64}R$

Option 3)

$\frac{3}{4}R$

Option 4)

$\frac{1}{16}R$

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