a) A copper wire has a diameter of 0.50 mm and a resistance of 1.6 × 10-8 Ω cm. what will be the length of this wire to make its resistance 10ohm. How much does the resistance change if the diameter is doubled?
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Explanation:
Given
diameter of the copper wire=0.5×10^-3 m
area (A)=3.14×0.5×10^-3×0.5×10^-3/4
=0.19 ×10^-6
=1.9× 10^-7 m^2
resistivity(p)=1.6×10^-10 ohm-m
Resistance (R)=10 ohms
length (l)= RA/p
=10×1.9×10^-7/1.6×10^-10
=1.18×10^4=11800m
If diameter is doubled
radius=0.5×10^-3m
area(A)=3.14×0.5×10^-3×0.5×10^-3
=7.8×10^-7 m^2
R=pl/A
=1.6×10^-10×1.18×10^4/7.8×10^-7
=2.5 ohms
Resistance is decreased by 4 times
change in resistance=10-2.5=7.5
Resistance is changed by 3/4 times
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