When an iron wire of diameter 1 cm is copper plated uniformly. Resistance of iron reduces to `1/3` of its original value. Calculate the thickness of copper plating, Resistivities of copper and iron are `1.8 times 10^-6 Omega`.cm and `1.98 times 10^-5 Omega`.cm respectively.

Explanation

Let resistance of iron wire be r and that of copper plating x.
As they are in parallel, so equivalent resistance , `R_(eq)=(rx)/(r+x)`
`therefore(rx)/(r+x)=r/3or,3rx=r^2+rxor,2rx=r^2`
`therefore x=r/2`
Now, `r=rhol/A=(1.98times10^-5timesl)/(pi(0.5)^2)`
Similarly , `x=(1.8times10^-6timesl)/(2pi(0.5)d)` (l=length , d= thickness)
Solving for r and x, it is observed that d=0.045 (approx)