Two metal wires of identical dimensions are connected in series. If...

Two metal wires of identical dimensions are connected in series. If

{v}_{1}

and

{v}_{2}

are the conductivities of the metal wires respectively, the effective conductivity if the combination is: Two metal wires of identical dimensions are connected in series. If v _ 1 and v _ 2 are the conductivities of the metal

Two metal wires of identical dimensions are connected in series. If v _ 1 and v _ 2 are the conductivities of the metal

Options

A $\dfrac{{\sigma}_{1} + {\sigma}_{2}}{2{\sigma}_{1}{\sigma}_{2}}$
B $\dfrac{{\sigma}_{1} + {\sigma}_{2}}{{\sigma}_{1}{\sigma}_{2}}$
C $\dfrac{{\sigma}_{1}{\sigma}_{2}}{{\sigma}_{1} + {\sigma}_{2}}$
D $\dfrac{2{σ}_{1}{σ}_{2}}{{σ}_{1} + {σ}_{2}}$

Correct answer

D. $\dfrac{2{σ}_{1}{σ}_{2}}{{σ}_{1} + {σ}_{2}}$

Step-by-step solution

Two metal wires of identical dimensions are connected in series. If v _ 1 and v _ 2 are the conductivities of the metal
${R}_{ec} = \dfrac{l}{{\sigma}_{1}A} + \dfrac{l}{{\sigma}_{1}A} = \dfrac{{l}_{eq}}{{\sigma}_{eq}{A}_{eq}}$
$\dfrac{2l}{{\sigma}_{eq}A} = \dfrac{l}{A}\left(\dfrac{{{\sigma}_{1} + \sigma}_{2}}{{\sigma}_{1}{\sigma}_{2}}\right)$
${\sigma}_{eq} = \dfrac{2{\sigma}_{1}{\sigma}_{2}}{{\sigma}_{1} + {\sigma}_{2}}$

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