Question

Find the equivalent resistance between $\text{A}$ and $\text{E}$ (Resistance of each resistor is $R$).

• A. $\frac{7}{12}R$
  
• B. $\frac{7}{13}R$
  
• C. $\frac{7}{15}R$
  
• D. $\frac{8}{13}R$
  

Answer 1

The correct option is A $\frac{7}{12}R$


In the given circuit, points $B$ and $I$ have same potential and points $D$ and $J$ have same potential.

Points, $B,I$ are in symmetry with points $D,J$.

Point $F$ is symmetric with point $H$.

Now, considering the symmetry points, the given circuit can be redrawn as follows,




The equivalent resistance of the given circuit is,

$R_{AE}=\frac{R\times \frac{7R}{5}}{R+\frac{7R}{5}}=\frac{7R}{12}$

Hence, option (a) is the correct answer.

Key concept : Point of symmetry Points having symmetric locations with respect to which input and output ends are of equal potential.