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A copper wire has diameter 0.5mm and res...

A copper wire has diameter 0.5mm and resistivity of `1.6xx10^(-8)Omega`m. what will be the length of this wire to make its resistance `10Omega`? How much does the resistance change if the diameter is doubled ?

Text Solution

Verified by Experts

Area of cross-section of the wire, A`=pi(d//2)2`
Resistance, R`=10Omega` We know that
`R=rho1/A`
`l=(RA)/rho=(10xx3.14xx25)/(4xx16)=122.72m`
length of the wire=122.72m
If the diameter of the wire is doubled, new diameter
`=2xx05=1mm=0.001m`
Let new resistance be R.
`R.=rho1/A=(1.6xx10^(-8)xx122.72)/(pi(1/2xx10^(-3))^2)=(1.6xx10^(-8)xx122.72xx4)/(3.14xx10^(-6))`
`=250xx10^(-2)=2.50`
Therefore, the length of the wire is 122. 7 m and the new resistance is `2.5Omega`
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