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) `
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Resistance of copper wire ` R_(cu) =rho_c (l)/(pi r^(2) `
`" " ( because A = pi r^(2)) `
Resistance of Nickle wire
` because " " A _(Ni) =pi (2r )^(2) -pir^(2) =3pir^(2) " "r " "R_(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 _crho_n)/(3rho_c+rho_n)) (l)/(pir^(2))`