Thank you for reporting, we will resolve it shortly
Q.
Two metallic wires of identical dimensions are connected is series. If $\sigma_1$ and $\sigma_2$ are the conductivities of the these wires respectively, the effective conductivity of the combination is :
Let length of wire be ' $\ell$ '
Area of wire as ' $A$ '
For equivalent wire length $=2 \ell \&$ area will be A
Thermal resistance
$ R _{ eq }= R _1+ R _2$
$\frac{2 \ell}{\sigma_{ eq } A }=\frac{\ell}{\sigma_1 A }+\frac{\ell}{\sigma_1 A }$
$ \frac{2 \ell}{\sigma_{ eq }}=\frac{\ell}{\sigma_1}+\frac{\ell}{\sigma_2} $
$\Rightarrow \sigma_{ eq }=\frac{2 \sigma_1 \sigma_2}{\sigma_1+\sigma_2}$
