A copper wire of length l and radius r is nickel plated till its final radius is 2r. If the resistivity of the copper and nickel are `rho_(c)` and `rho_(n)`, then find the equivalent resistance of the wire.

Explanation

`R=rho(l)/(A)`
Resistance of copper wire `R_(Cu)=rho_(c)(l)/(pir^(2))(because A=pir^(2))`
Resistance of Nickle wire `because A_(Ni)=pi(2r)^(2)-pir^(2)=3pir^(2)rArrR_(Ni)=rho_(n)(l)/(3pir^(2))`
Both wire are connected in parallel, so equivalent resistance `R=(R_(Cu)R_(Ni))/(R_(Cu)+R_(Ni))=((rho_(C)rho_(n))/(3rho_(C)+rho_(n)))(l)/(pir^(2))`