A copper wire has diameter 0.5 mm and activity of 1.6 into 10 power minus 8 mwhat will be the length of this wire to make its resistance 40 metre? how much does the resistance change if the diameter is doubled
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Answer:
Given, diameter, d=0.5 mm
resistivity, ρ=1.6×10
−8
Ωm
Resistance, R=10 Ω
Let the length of wire be l.
A=πd
2
/4
R=ρl/A
=
πd
2
/4
ρl
⟹l=
4ρ
Rπd
2
l=
4×1.6×10
−8
10×3.14×(0.5×10
−3
)
2
l=122 m
R∝1/d
2
If the diameter is doubled, resistance will be one-fourth.
Hence, new resistance =2.5Ω
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