Answer to Question #91879 in Electric Circuits for Priskilla

Question #91879
A 6.0m long wire having a diameter of 2.0 mm has a resistance of 12.2 m ohm. A potential difference of 23V is applied between the ends. Calculate the current in wire, the magnitude of the current density and the resistivity of the wire material
1
Expert's answer
2019-07-23T15:53:32-0400

According to the Ohm's law, the current in a wire is


I=VRI = \frac{V}{R}

Substituting the numerical values, we obtain:


I=23V12.2103Ω1.89103AI = \frac{23 \, V}{12.2 \cdot 10^{-3} \, \Omega} \approx 1.89 \cdot 10^3 \, A

The current density is a current flowing through a unit cross-sectional area of a wire:


j=IS=4Iπd2j = \frac{I}{S} = \frac{4 I}{\pi d^2}

Substituting the numerical values, we obtain:


j=41.891033.14221066.0108Am2j = \frac{4 \cdot 1.89 \cdot 10^{3}}{3.14 \cdot 2^2 \cdot 10^{-6}} \approx 6.0 \cdot 10^8 \frac{A}{m^2}

The resistivity of a wire material is:


R=ρlSρ=RSl=Rπd24lR = \rho \frac{l}{S} \, \Rightarrow \, \rho = \frac{R S}{l} = \frac{R \pi d^2}{4 l}

Substituting the numerical values, we obtain:


ρ=12.21033.1422466.3103Ohmmm2m\rho = \frac{12.2 \cdot 10^{-3} \cdot 3.14 \cdot 2^2}{4 \cdot 6} \approx 6.3 \cdot 10^{-3} \, \frac{Ohm \cdot mm^2}{m}


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