A wire of resistance R is bent to form a square A B C D as shown in the figure.


A wire of resistance $R$ is bent to form a square $A B C D$ as shown in the figure. The effective resistance between $\mathrm{E}$ and $C$ is: $(E$ is mid-point of arm $C D)$


  1. (1) $\mathrm{R}$

  2. (2) $\frac{7}{64} \mathrm{R}$

  3. (3) $\frac{3}{4} \mathrm{R}$

  4. (4) $\frac{1}{16} R$

Correct Option: , 2


(2) Here $\mathrm{R}_{\mathrm{DA}}=\mathrm{R}_{\mathrm{AB}}=\mathrm{R}_{\mathrm{BC}}=\mathrm{R} / 4$

and $\mathrm{R}_{\mathrm{DE}}=\mathrm{R}_{\mathrm{EC}}=\mathrm{R} / 8$

Now $R_{E D}, R_{D A}, R_{A B}, R_{B C}$ are in series.

$\therefore R_{s}=\frac{R}{8}+\frac{R}{4}+\frac{R}{4}+\frac{R}{4}=\frac{R+2 R+2 R+2 R}{8}=\frac{7 R}{8}$

$\therefore \mathrm{R}_{\mathrm{eq}}=\frac{\left(\frac{7 R}{8}\right)\left(\frac{R}{8}\right)}{R}=\frac{7 R}{64}$

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