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Question
What length of a copper wire of cross-sectional area 0.01 mm2 will be needed to prepare a resistance of 1 kΩ? Resistivity of copper = 1.7 × 10–8 Ωm
Solution
Given:-
Resistivity of copper, ρcu = 1.7 × 10–8 Ωm
Area of cross-section, A = 0.01 mm2 = 0.01 × 10–6 m2
Required resistance, R = 1 kΩ = 103 Ω
Let l be the required length of the copper wire.
We know:-
\[R = \frac{\rho l}{A}\]
\[ \Rightarrow l = \frac{RA}{\rho_{cu}}\]
\[ \Rightarrow l = \frac{{10}^3 \times 0 . 01 \times {10}^{- 6}}{1 . 7 \times {10}^{- 8}}\]
\[ \therefore l = 0 . 58 \times {10}^3 m = 0 . 6 km\]
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