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]

Let length of each side of square ABCD is “a”

$\therefore$resistance per unit length of each side$=\frac{R}{4a}$

Now ,  $R_1=\frac{R}{4a}\left(EC\right)=\frac{R}{4a}\left(\frac{a}{2}\right)=\frac{R}{8}$

Similarly $R_2=\frac{R}{4a}\left(EDAB\right)=\frac{R}{4a}\times \frac{7a}{2}=\frac{7R}{8}$

$\therefore$ effective resistance between E and C is

${\mathrm{R}}_{eff}=\frac{R_1{R}_2}{R_1+R_2}=\frac{\frac{R}{8}\times \left(\frac{7R}{8}\right)}{\frac{R}{8}+\left(\frac{7R}{8}\right)}=\frac{7}{64}R$