Determine the cross-sectional area of the copper wire.
$$ \begin{aligned} A &=\pi\left(\frac{d}{2}\right)^{2} \\ &=\pi\left(\frac{0.100 \mathrm{~mm}\left(\frac{10^{-3} \mathrm{~m}}{1 \mathrm{~mm}}\right)}{2}\right)^{2} \\ &=7.854 \times 10^{-9} \mathrm{~m}^{2} \end{aligned} $$
The resistance of the copper wire is,
$$ \begin{aligned} R &=\frac{\rho L}{A} \\ &=\frac{\left(1.68 \times 10^{-8} \Omega \cdot \mathrm{m}\right)(1.60 \mathrm{~m})}{7.854 \times 10^{-9} \mathrm{~m}^{2}} \\ &=3.42 \Omega \end{aligned} $$
Here, \(\rho\) is the resistivity of the wire and \(L\) is the length of the wire.
(2)
Determine the cross-sectional area of the carbon wire.
$$ \begin{aligned} A &=\left(1.00 \mathrm{~mm}\left(\frac{10^{-3} \mathrm{~m}}{1 \mathrm{~mm}}\right)\right)^{2} \\ &=1.00 \times 10^{-6} \mathrm{~m}^{2} \end{aligned} $$
The resistance of the carbon wire is,
$$ \begin{aligned} R &=\frac{\rho L}{A} \\ &=\frac{\left(3.5 \times 10^{-5} \Omega \cdot \mathrm{m}\right)\left(90.0 \mathrm{~cm}\left(\frac{10^{-2} \mathrm{~m}}{1 \mathrm{~cm}}\right)\right)}{1.00 \times 10^{-6} \mathrm{~m}^{2}} \\ &=31.5 \Omega \end{aligned} $$
What is the resistance a 1.60m long copper wire that is 0.100mm in diameter? A 90.0...
What is the resistance of A) A 0.800 m long copper wire that is 0.700 mm in diameter? B) A 90.0 cm long piece of carbon with a 0.500 mm × 0.500 mm square cross section?
What is the resistance of a. A 1.60 m long copper wire that is 0.600 mm in diameter? b. A 70.0 cm long piece of carbon with a 1.60 mm × 1.60 mm square cross section?
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Part A What is the resistance of a 1.5-m-long copper wire that is 0.30 mm in diameter? Submit My Answers Give Up Part B What is the resistance of a 10-cm-long piece of iron with a 1.5 mm x 1.5 mm square cross section? Express your answer using two significant figures Submit My Answers Give Up
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