`rho_1` and `rho_2` are the resistivities of the materials of two wires of the same dimensions, what will be the equivalent resistvity of the series combination of the two wires?

Explanation

Let l be the length and A be the cross sectional area of each wire.
The equivalent resistance in series combination , is
`R=R_1+R_2=rho_1 1/A+rho_2 1/A=(rho_1+rho_2)1/A........(1)`
In the series combination, length of the conductor =2 l, cross sectional area=A. Let the equivalent resistivity be `rho`.
`therefore R=rho (2l)/A` ..........(2)
Comparing (1) and (2) we have,
`rho(2l)/A=(rho_1+rho_2)1/Aor,(rho1+rho_2)/2`