Two wires of equal diameters of resistivities `p_1 and p_2` and length` 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_(1)=x_(1), l_(2)=x_(2)`
As the wires are of equal diameters `A_(1)=A_(2)=A`.
`R_(1)=(rhox_(1))/(A), R_(2)=(rhox_(2))/(A_(2)),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))" also "=(1)/(sigma)=(sigma_(1)+sigma_(2))/(x_(1)+x_(2))`