Question 199: Current Electricity

Question

Two metallic wires of identical dimensions are connected in series. If $$\sigma_{1}$$ and $$\sigma_{2}$$ are the conductivities of the these wires respectively, the effective conductivity of the combination is :

Accepted Answer

$$R = {R_1} + {R_2}$$
$$ \Rightarrow {{{l_1} + {l_2}} \over {\sigma A}} = {{{l_1}} \over {{\sigma _1}A}} + {{{l_2}} \over {{\sigma _2}A}}$$
$$ \Rightarrow {2 \over \sigma } = {1 \over {{\sigma _1}}} + {1 \over {{\sigma _2}}}$$
$$ \Rightarrow \sigma  = {{2{\sigma _1}{\sigma _2}} \over {{\sigma _1} + {\sigma _2}}}$$

Answer

$$
\frac{\sigma_{1} \sigma_{2}}{\sigma_{1}+\sigma_{2}}
$$

Answer

$$
\frac{2 \sigma_{1} \sigma_{2}}{\sigma_{1}+\sigma_{2}}
$$

Answer

$$
\frac{\sigma_{1}+\sigma_{2}}{2 \sigma_{1} \sigma_{2}}
$$

Answer

$$
\frac{\sigma_{1}+\sigma_{2}}{\sigma_{1} \sigma_{2}}
$$

Current Electricity

Two metallic wires of identical dimensions are connected in series. If $\sigma_{1} and \sigma_{2}$ are the conductivities of the these wires respectively, the effective conductivity of the combination is :

Choose the correct answer: