Question

Two resistances are made of same material having the same area of cross section and length of one wire is double of another wire are connected in parallel. If you are not provided with any other parameters (eg. numerical values of I and V), what can you say about the resistivity of two resistors?
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Answer 1

Answer:

Resistivity is denoted by "ρ". Here since the resistors are made of same material then the resistivity would be same as resistivity is the property of the element and is independent of the dimensions. If you are interested in the combined resistance of the two resistors in parallel then Rᵣₑₛ=

$Rᵣₑ= \frac{2l}{3}$

Answer 2

Given:

Area of cross section of both wires is same

Length of one wire = 2* Length of another wire

To find:

What can be said about the resistivity of two resistors.

Solution:

Let the two wires be A and B

Let the area of cross section of wires (A and B)= A

Length of wire (A) = L

Length of Another wire (B) = 2L

We know that resistance R = ρL/A

Where ρ is the resistivity,

L is the length,

A is the cross-sectional area.

Two wires of same material have same resistivity as resistivity is intrinsic property of the material of the wire.

But resistance of wire A = ρL/A

Resistance of wire B =2ρL/A

Therefore the resistance of wire B is double of that of wire A.

The resistivity of second wire is the same as that of the resistivity of first wire as their materials are same.