There are three copper wires of length and cross sectional area area [ L, A ], [a2L,A/2 ] [L/2A] In which case is the resistance minimum?
a) it is the same in all three cases
b) wire of cross sectional area 2A
c) wire of cross section area A
d) wire of cross section the area 1/2 A
Answers
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19
Q]_____?
=> Option B
Explanation:
The relation between length and area is
R = ρl / A _[i]
where, ρ being specific resistance is the proportionality constant and depends on the nature of material
[i]
Length = L/2, area = 2A
Putting in equation [i], we have
R = ρ (L/2) / 2A = ρ L/4A
[ii]
Length = L, area = A/2
Putting in Eq [i] we have
R = ρL/A
[iii]
Length = 2L, area = A/2
Putting in Eq [i] we have
R =ρ2L / ( A/2 ) = 4ρL / A
As it is understood from above resistance is minimum only in option B !
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