# The resistances in the following figure are in ohm. Then the effective resistance between the points A and B is? (A) 2Omega (B) 3 Omega (C) 6Omega (D) 36 Omega

In the given network for resistor if we consider the portion ACD , we observe that across AD resistor ${R}_{A C}$ and ${R}_{C D}$are in series and ${R}_{A D}$ is parallel . So the equivalent resistance of this portion across AD becomes
${R}_{\text{eqAD}} = \frac{1}{\frac{1}{{R}_{A C} + {R}_{C D}} + \frac{1}{R} _ \left(A D\right)} = \frac{1}{\frac{1}{\left(3 + 3\right)} + \frac{1}{6}} = 3 \Omega$
and we get equivalent network $\textcolor{red}{2}$
similarly if we proceed , we finally reach at figure $\textcolor{red}{4}$ i.e.equivalent network $A B F$ and the equivalent resistance of the given network across AB becomes
${R}_{\text{eqAB}} = = \frac{1}{\frac{1}{{R}_{A F} + {R}_{F B}} + \frac{1}{R} _ \left(A B\right)} = \frac{1}{\frac{1}{\left(3 + 3\right)} + \frac{1}{3}} = 2 \Omega$