A 4 `Omega ` resistance wire is doubled on it. Calculate the new resistance of the wire.

Explanation

We are given, R = 4`Omeag `.
When a wire is doubled on it, its length would become half and area of cross-section would double. That is, a wire of length l and area of cross-section A becomes of length l/2 and area of cross- section 2A. From Eq. (12.10), we have
`R= rho (l)/(A)`
`R_1 = rho =((l//2))/((2A))`
where `R_1 ` is the new resistance .
therefore ` (R_1)/(R)=rho = (l//2)/(2A) //rho (l)/(A) = 1/4 `
or ` R_1 = (R )/(4) = ( 4 Omega )/( 4) = 1 Omega `