Question

An aluminium wire and a tungsten wire of the same lengths have the same p.d applied across them. If their resistivities are in the ratio 1 : 2 , for the currents in the wires to be the same , the ratio of their radii must be about......... 
a) 0.5
b)0.7
c) √2
d) 2
e) Other​

Answer 1

Answer:

Resistivity of aluminium, ρAI=2.63×10−8Ωmρ

Relative density of aluminium, d1=2.7

Let l1 be the length of aluminium wire and m 1 be its mass.

Resistance of the aluminium wire =R1

Area of cross-section of the aluminium wire =A1

Resistivity of copper, ρCu=1.72×10−8Ωm

Relative density of copper, d2=8.9

Let l2 be the length of copper wire and m 2 be its mass.

Resistance of the copper wire =R2

Area of cross-section of the copper wire =A2

The two relations can be written as

R1=ρ1A1l1  ...(1)

R2=ρ2A2l2  ...(2)

It is given that,

R1=R2

∴ρ1A1