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A wire of 10 ohm resistance is stretched...

A wire of 10 ohm resistance is stretched to thrice its original length. What will be its (i) new resistivity and (ii) new resistance?

Text Solution

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(i) Resistivity `rho` remains unchanged because it is the property of the material of the wire.
(ii) In both cases, volume of wire is same, so
`V=A.l.=Al`
`(A.)/(A)=(l)/(l.)=(l)/(3l)=(1)/(3)" " [because l.=l+2l=3l]`
`therefore (R.)/(R )=(rho(l.)/(A.))/(rho (l)/(A))=(l.)/(l)xx(A)/(A.)=(3)/(1)xx(3)/(1)=9`
Hence, `R.=9R=9xx 10=90Omega`
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