(i) Find the equivalent resistance between A and B.

(ii) State whether the resistivity of a wire changes with the change in the thickness of the wire.

(i) In figure, a parallel combination of resistors 6 Ω and 3 Ω are connected in series with another parallel combination of resistors 4 Ω and 12 Ω between the terminals A and B.

In the first part, let the equivalent resistance of parallel combination of resistors 3 Ω and 6 Ω be R₁.

$\dfrac{1}{R$1} = \dfrac{1}{3} + \dfrac{1}{6} \\[0.5em] \Rightarrow \dfrac{1}{R1} = \dfrac{2 + 1}{6} \\[0.5em] \Rightarrow \dfrac{1}{R1} = \dfrac{3}{6} \\[0.5em] \Rightarrow \dfrac{1}{R1} = \dfrac{1}{2} \\[0.5em] \Rightarrow R_1 = 2 Ω

In the second part, 4 Ω and 12 Ω are in parallel connection. If the equivalent resistance is R₂ then

$\dfrac{1}{R$2} = \dfrac{1}{4} + \dfrac{1}{12} \\[0.5em] \Rightarrow \dfrac{1}{R2} = \dfrac{3 + 1}{12} \\[0.5em] \Rightarrow \dfrac{1}{R2} = \dfrac{4}{12} \\[0.5em] \Rightarrow \dfrac{1}{R2} = \dfrac{1}{3} \\[0.5em] \Rightarrow R_2 = 3 Ω

In the third part R₁ and R₂ are in series. Therefore we get,

2 + 3 = 5 Ω

Hence, equivalent resistance between A and B = 5 Ω.

(ii) The resistivity of wire does not change with the change in the thickness of the wire.