A copper wire of diameter 0.5 mm and resistivity of 1.6 × 10-⁸ ohm meter. What will be the length of the wire to make it resistance 10 ohm ? How much does the resistance changes when the diameter is doubled ?
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Answer:
Therefore, the length of the wire is 122.7 m and the new resistance becomes 1/4 times.
Explanation:
Find out
We have to find the length of the wire
Let the length of the wire be L
Formula
We know that
R = ρ (L) / (A)
L = (R × A) / ρ
Substituting the values in the above equation we get
L = (10 × 1.964 × 10⁻⁷) / 1.6 × 10⁻⁸ m
L = 1.964×10-6 /1.6 × 10-8
L = 122.72 m
If the diameter of the wire is doubled, the new diameter = 2 × 0.5 = 1mm = 0.001m
Let new resistance be Rʹ
R = ρ (L) / (A)
R’ = ρ (L) / (4A)
R’ = ρ (L) X 1/(4A)
Hence, if diameter doubles, resistance becomes 1/4 times.
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