Calculate the effective resistance between the points A and B in the network shown below in figure.

In the circuit, there are two parts. In the first part, resistors of 12 Ω, 6 Ω and 4 Ω are connected in parallel. If the equivalent resistance of this part is R'_p then

$\dfrac{1}{{R'}$P} = \dfrac{1}{12} + \dfrac{1}{6} + \dfrac{1}{4} \\[0.5em] \dfrac{1}{{R'}P} = \dfrac{1 + 2 + 3}{12} \\[0.5em] \dfrac{1}{{R'}P} = \dfrac{6}{12} \\[0.5em] \dfrac{1}{{R'}P} = \dfrac{1}{2} \\[0.5em] \Rightarrow {R'}_P = 2 Ω

Hence, R'_P = 2 Ω

In the second part, resistors of 2 Ω, (R'_p = 2Ω) and 5 Ω are connected in series. If the equivalent resistance of this part is R_s then

R_s = (2 + 2 + 5) Ω = 9 Ω

Hence, Effective resistance between A and B = 9 Ω