Question

Calculate equivalent resistance between $A$ and $B$ of the circuit shown in Figure

Answer 1

Equivalent circuit of the above figure is shown.

Equivalent resistance between E and F $R_{EF}=(9+9)\parallel 9=18\parallel 9=\frac{9\times 18}{9+18}=6\Omega$

Equivalent resistance between C and D $R_{CD}=(12+R_{EF}+12)\parallel (15+15)=30\parallel 30=15\Omega$

Equivalent resistance between I and J $R_{IJ}=(3+3)\parallel 3=18\parallel 9=\frac{3\times 6}{3+6}=2\Omega$

Equivalent resistance between G and H $R_{GH}=(4+R_{IJ}+4)\parallel (5+5)=10\parallel 10=5\Omega$

$\therefore$ Equivalent resistance between A and B $R_{AB}=(2+R_{GH}+2)\parallel (6+R_{CD}+6)=9\parallel 27$

$⟹$ $R_{AB}=\frac{9\times 27}{9+27}=6.75\Omega$