Question

If the equivalent resistance of the circuit between points $A$ and $B$ shown on figure is $\frac{x}{35}\Omega$. Find $11x$. (each branch is of resistance = $1\Omega$)

Answer 1

The outermost branches can easily be reduced to the ones shown in the figure by visualizing them to be in simple series and parallel combinations.

Now,through symmetry of the circuit, the whole circuit can be assumed to have current flowing as shown.

Appying Kirchoff' current law at above node gives

$I_1=I_4+I_3$

Also from Kirchoff's Voltage Law,

$I_3-\frac{2}{3}{I}_4+I_3=0$

and $I_2=\frac{2}{3}{I}_1+I_3$

Hence,$I_2=\frac{11}{12}{I}_1$

From Kirchoff's Voltage Law

$V_A-V_B=\left(1\right)I_2+\left(1\right)I_2=(I_2+2I_1)R_{eq}$

hence $R_{eq}=\frac{22}{35}$