Two wires of equal diameters of resistivities `rho_1`. and `rho_2` , lengths `X_1 and X_2` respectively are joined in series. The equivalent resistivity of the combination is

Explanation

Resistance , `R_1 = (rho_1 l_1)/(A_1) , R_2 = (rho_2 l_2)/(A_2)`
`l_2 = x_1 , l_2 = x_2`
As the wires are of equal diameters `A_1 = A_2 = A`.
`R_1 = (rho_1 x_1)/(A) , R_2 = (rho_2 x_2)/(A)`
`R= (rhox)/(A)`
where `x= x_1 + x_2`
`R= R_1 + R_2`
`(rhox)/(A) = (rho_1 x_1)/(A) + (rho_2 x_2)/(A)`
`rhox = rho_1 x_1 + rho_2 x_2`
`rho (x_1 + x_2) = rho_1 x_1 + rho_2 x_2 [ because x= x_1 + x_2]`
`therefore rho = (rho_1 x_1 + rho_2 x_2)/(x_1 + x_2)`