CBSE Class 10 Science 2022 Outside Delhi Term II Set 3

Question : 4

Total: 7

(a) Write the relationship between electrical resistance and electrical resistivity for a metallic conductor of cylindrical shape. Hence derive the SI unit of electrical resistivity.
(b) Find the resistivity of the material of a metallic conductor of length 2m and area of cross-section 1.4×10−6m2. The resistance of the conductor is 0.04‌ohm.

Solution:

(a) Resistance of a uniform metallic conductor is directly proportional to its length (l) and inversely proportional to the area of cross-section (A).
i.e.,
R∝1
and
R∝‌

Combining equations. (i) and (ii) we get or
‌R∝‌

‌R=ρ‌

where ρ (rho) is a constant of proportionality and is called the electrical resistivity of the material of the conductor. Now, putting the units of R,A and l in the expression.
ρ‌=‌

Ωm2

‌=Ω−m
Thus, the S.I unit of resistivity is Ohmmeter (Ω−m).
(b) Given
Resistance R=0.04‌ohm
Area of cross section A=1.4×10−6m2
Length ‌‌l=2m
Using the formula,
R=ρ‌

Resistivity ρ can be calculated as
P‌=(R×A)∕l
‌ So resistivity ‌=‌(0.04×1.4×10−6m2)∕2m
‌=2.8×10−8‌Ohm‌-meter ‌

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