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You need to produce a set of cylindrical copper wires 2.5 m long that will have a resistance of `0.125Omega` each. What will be the mass of each of these wires? (Density of copper is `8.9xx10^3 kgm^(-3)` and resistivity of copper is `1.72 xx10^(-8) Omegam).`

Text Solution

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Given the `L = 2.5 m R = 0.125 Omega.` To find the mass of
each wire, we need to calculate the volume of one of the wires.
`"Mass" = "Density"xx"Volume"`
Volume = Areaxx Length `[:. R = (rhoL)/(A) or A =(rhoL)/(R )]`
Volume `= AL=(rhoL^2)/(R )=(1.72xx10^(-8)xx(2.5)^2)/(0.125)=8.6xx10^(-7) m^3`
`m = dxxV = 8.9xx10^3xx8.6 xx10^(-7)`
`=7.654xx10^(-3)kg = 7.654 g`
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