Current Electricity — Question 11

Let the four set of resistors be R₁, R₂, R₃, R₄ .

As each set consists of three resistors of 2 Ω each in series:
Resistance of each set = 2 + 2 + 2 = 6 Ω

As four similar sets of equivalent resistance 6 Ω are arranged in parallel, so the equivalent resistance (R_P) will be:

$\dfrac{1}{R_P} = \dfrac{1}{R_1} + \dfrac{1}{R_2} + \dfrac{1}{R_3} + \dfrac{1}{R_4} \\[0.5em] \dfrac{1}{R_P} = \dfrac{1}{6} + \dfrac{1}{6} + \dfrac{1}{6} + \dfrac{1}{6} \\[0.5em] \dfrac{1}{R_P} = \dfrac{4}{6} \\[0.5em] R_P = \dfrac{6}{4} \\[0.5em] \Rightarrow R_P = 1.5 Ω$

Hence, equivalent resistance = 1.5 Ω