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 :
Solution
<p>$R = {R_1} + {R_2}$</p>
<p>$$ \Rightarrow {{{l_1} + {l_2}} \over {\sigma A}} = {{{l_1}} \over {{\sigma _1}A}} + {{{l_2}} \over {{\sigma _2}A}}$$</p>
<p>$$ \Rightarrow {2 \over \sigma } = {1 \over {{\sigma _1}}} + {1 \over {{\sigma _2}}}$$</p>
<p>$$ \Rightarrow \sigma = {{2{\sigma _1}{\sigma _2}} \over {{\sigma _1} + {\sigma _2}}}$$</p>
About this question
Subject: Physics · Chapter: Current Electricity · Topic: Ohm's Law and Resistance
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