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For finding the specific resistance of a...

For finding the specific resistance of a wire, a student took the following readings by using a metre scale, a micrometer and a resistance box.
Length of the wire (L) = 100.0 cm
Radius (r ) = 0.100 cm and R = `10 Omega`
What is the maximum possible percentage error in the value of the specific resistance?

A

`9.8%`

B

`12.1%`

C

`15.5%`

D

`18%`

Text Solution

Verified by Experts

The correct Answer is:
b
`because R=(rhoL)/(A)`
`therefore` Specific resistance `(rho)=(RA)/(L)=(Rpir^(2))/(L)`
`therefore (Deltarho)/(rho)xx100=((DeltaR)/(R)+2(Deltar)/(r)+(DeltaL)/(L))xx100`
But `DeltaR=1Omega,dr=0.001cm, dL=0.1cm`
`therefore ((Deltarho)/(rho))xx100=((1)/(10)+(2xx0.001)/(0.1)+(0.1)/(100))xx100`
`=10+2+0.1=12.1%`
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