A resistance wire has a resistance R. Half of the wire is stretched to double its length and half is twisted to double its thickness. Find the value of new resistance.

Explanation

If l is length , a is area , `rho` is resistivity , then resistor R of wire is `R = rho (l)/(a )`
Now , according to question let A and B are two pieces.

Now , according to questions
`R_(A) = (rho(2l))/(a//2) = (4pl)/(a)` [as lenght is doubled , then area will be haveled].
`R_(A) = 4R`
`R_(B) = (rho ((L)/(8)))/(4a)`
[ as thickness will be doubled , then area will be 4 times and lenght will be `(1)/(8)` times].
` = (R)/(32)`
Total new resistance `= R_(A) + R_(B)`
` = 4R + (1)/(32) R = (129)/(32)R`