Three wires, A, B and C, of the same length and the same thickness have resistances of 1 Ω, 0.5 Ω and 0.25 Ω, respectively. Their resistivities are ____________.

Correct option is C

Given:

All wires  A , B , and  C  have the same length  L  and same thickness so  A  is the same for all wires.

Formula used:

The resistance of a wire is related to its resistivity:

​$$R = \rho \frac{L}{A}$$ 

where:

R is the resistance,

$$\rho$$​ is the resistivity,

L is the length of the wire,

A is the cross-sectional area.

Solution:

Resistances are:

​$$R_A = 1 \, \Omega, \, R_B = 0.5 \, \Omega, \, R_C = 0.25 \, \Omega$$ 

Since $$\rho \propto R$$ (as L and  A are constant):

$$\rho_A : \rho_B : \rho_C = R_A : R_B : R_C = 1 : 0.5 : 0.25$$ 

Simplify the ratio:

$$\rho_A : \rho_B : \rho_C = 4 : 2 : 1$$ 

Thus the correct answer is (C)