A current of 12.5 mA is carried via a copper wire of 14-gauge with a diameter of 1.628 mm.(a) What is the potential difference across a 2.00-m length of the wire?&nbsp;(b) What would the potential difference in part (a) be if the wire were silver instead of copper, but all else were the same?

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A current of 12.5 mA is carried via a copper wire of 14-gauge with a diameter of 1.628 mm.(a) What is the potential difference across a 2.00-m length of the wire?&amp;nbsp;(b) What would the potential difference in part (a) be if the wire were silver instead of copper, but all else were the same?

autormtak0w · Accepted Answer

Step 1  Given that:  d=1.628mm=1.628×10−3m,I=12.5mA=12.5×10−3A  The Cross-sectional area of the wire is:  A=π4d2  =π4×(1.628×10−3m)2  =2.082×10−6m2  a) The Potential difference across a 2.00m length of a 14-gauge copper wire:  L=2.00m  From Table 25.1: Copper Resistivity ρ=1.72×10−8Ω⋅m  The Resistance of the Copper wire is:  R=ρLA  =(1.72×10−8Ω⋅m)(2.00m)2.082×10−6m2  =0.0165Ω  The Potential difference across the copper wire is:  V=IR  =(12.5×10−3A)×(0.0165Ω)  =2.063×10−4V  Step 2  b) The Potential difference if the wire were made of Silver:  From Table 25.1: Silver Resistivity ρ=1.47×10−8Ω⋅m  The Resistance of the Silver wire is:  R=ρLA  =(1.47×10−8Ω⋅m)(2.00m)2.082×10−6m2  =0.014Ω  The Potential difference across the Silver wire is:  V=IR  =(12.5×10−3A)×(0.014Ω)  =1.75×10−4V

Barbara Meeker · Accepted Answer

Step 1  The diameter of the copper wire is, d=1.628mm=1.628×10−3m  The current carried by the wire is 12.5 mA, I=12.5×10−3A  The resistance across a wire of length L and cross sectional area A is given as R=ρLA  ρ is the resistivity of the material  The length of the wire is, L=2m  The cross sectional area of the wire will be  A=πr2  r is the radius of the wire, r=d2=0.814×10−3m  A=π(0.814×10−3)2  A=2.0816×10−6m2  Step 2  For copper, ρ=1.68×10−8Ωm  R=1.68×10−8×22.0816×10−6  R=0.016Ω  This is resistance for the given copper wire  From Ohms

A 14-gauge copper wire of diameter 1.628 mm carries a current of 12.5

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