(a) 1 : 1
(b) 1 : 2
(c) 1 : 4
(d) 1 : 8
Correct Answer: (a) 1
: 1
Explanation
Specific resistance (resistivity) depends only on
material, not dimensions.
Notes for
More Information
Specific Resistance
(Resistivity)
1. Specific
resistance, also called resistivity, is denoted by ρ.
2. Resistivity
is an intrinsic (material) property.
3. It depends
only on:
·
The nature/composition of the material
·
The temperature
4. It does
not depend on:
·
Length of the wire
·
Cross-sectional area of the wire
Given Relation
5. The
resistance of a wire is given by:
where:
·
= resistance
·
= resistivity
·
= length
·
= cross-sectional area
Case: Two Wires of the Same
Material
6. Since both
wires are made of the same material:
·
Their resistivity is the same.
7. Therefore:
8. Hence,
the ratio of their specific resistances (resistivities) is:
Important Clarification (Common
Confusion)
9. Even if:
·
Lengths are the same
·
Resistances are the same
·
Cross-sectional areas are different (e.g., 
)
10.
Resistivity will still remain the same, because
it depends only on the material, not on dimensions.
11.
The change in resistance due to area is already accounted for by the
term 
, not by ρ.
Key Point to Remember
12.
Resistance changes with length and area, but resistivity
does not.
13.
Therefore, for wires of the same material and same temperature:
Additional Information
14.
Low resistivity → material allows current
easily
- Example: Copper, Aluminum
15.
High resistivity → material opposes current
- Example: Rubber, Glass
16.
In metals, resistivity increases with temperature.
17.
Semiconductors have resistivity values
between conductors and insulators and can be controlled by:
- Temperature
- Doping
Final Conclusion
18.
Since resistivity is a material property, the ratio of
specific resistance of two wires made of the same material is:
