A. The resistance of a Im long
nichrome wire is 6 . If we reduce
the length of the wire to 70 cm.
what will its resistance be?
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A. The resistance of a Im long
nichrome wire is 6 . If we reduce
the length of the wire to 70 cm.
what will its resistance be?
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Verified answer
We are assuming that the volume of the wire isn't changing
Its given that
L₁=100 cm
L₂=70 cm
R₁=6 ohm
R₂=R₂
We know that
R=ρL/A
where
ρ=resistivity of the material
L=lenght of the wire
A=area of the wire
Volume of the wire is same therefore
V₁=V₂
A₁L₁=A₂L₂
A₁/A₂=L₂/L₁
=7/10
or
A₂/A₁=10/7
R₁=ρL₁/A₁
R₂=ρL₂/A₂
dividing the above two equations
R₁/R₂=L₁/L₂*A₂/A₁
=10/7*10/7
=100/49
R₂=R₁*49/100
=6*49/100
=2.94 ohm
If volume isn't the same after reducing the lenght we can directly say that
R₁/R₂=L₁/L₂
Since A and ρ are constant therefore the ratio becomes independent of it.
R₂=R₁*L₂/L₁
=6*70/100
=4.2 ohm
Hope this helps