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The electric resistance of a certain wir...

The electric resistance of a certain wire of iron is R. If its length and radius are both doubled, then

A

the resistance will be halved and the specific resistance will remain unchanged.

B

the resistance will be doubled and the specific resistance will be halved.

C

the resistance will be halved and the specific resistance will be doubled.

D

the resistance and the specific resistance will both remain unchanged.

Text Solution

Verified by Experts

The correct Answer is:
A
original resistance
`R= rho .(l)/(A) = rho .(l)/(pi r^(2))`
when both length and radius are doubled,
`R.=rho .(2l)/(pi(2r)^(2)) = (1)/(2) rho . (1)/(pir^(2)) = (1)/(2)R`
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