Question

What is the relative resistivity of Aluminum compared to Copper if copper resistivity is 1 (one)?
1. 2.8
2. 1.6
3. 4.4
4. 0.94

Answer 1

Correct Answer - Option 2 : 1.6

Concept of Electrical Resistivity:

• The electrical resistivity of particular conductor material is a measure of how strongly the material opposes the flow of electric current through it.
• Its unit is Ωm. 

​The resistance of a given conductor is given by:

\(R = ρ \frac{l}{A}\)

ρ = Resistivity of the conductor

l = length of the conductor

A = Area of the cross-section

Explanation:

• The area of cross-section of a conductor made of material other than copper is not specified by its actual value.
• Let the suffix a and c be used for aluminum and copper respectively.
• For the same length and resistance of aluminum and copper conductors,

R_a = R_c

\({ρ _a}\frac{l}{{{A_a}}} = {ρ _c}\frac{l}{{{A_c}}}\)

\({A_c} = \frac{{{ρ _c}}}{{{ρ _a}}}{A_a}\)

\(= \frac{1}{{\left( {\frac{{{ρ _a}}}{{{ρ _c}}}} \right)}}\left( {\begin{array}{*{20}{c}} {Cross - sectional\;area\;}\\ {of\;aluminium\;conductor} \end{array}} \right)\)

\( = \frac{1}{{1.62}}\left( {\begin{array}{*{20}{c}} {Cross - sectional\;area}\\ {\;of\;aluminium\;conductor} \end{array}} \right)\)

Since,\(\frac{{{ρ _a}}}{{{ρ _c}}} = 1.62\)

Here, ρ_c = 1 

So, \(\frac{{{ρ _a}}}{{{1}}} = 1.62\)

ρ_a = 1.62

​

 Some standard Electrical resistivity of material:

Material	Electrical Resistivity  OHM meters
Aluminum	2.8 × 10-8
Antimony	3.9 × 10-7
Bismuth	1.3 × 10-6
Brass	0.6 – 0.9 × 10-7
Cadmium	6 × 10-8
Cobalt	5.6 × 10-8
Copper	1.7 × 10-8
Gold	2.4 × 10-8
Carbon (Graphite)	1 × 10-5
Germanium	4.6 × 10-1
Iron	4.6 × 10-1
Lead	1.0 × 10-7
Manganin	4.2 × 10-7
Nichrome	1.1 × 10-7
Nickel	7 × 10-8
Palladium	1.0 × 10-7
Platinum	0.98 × 10-7
Quartz	7 × 1017
Silicon	6.4 × 102