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Home » Two metal wires of identical dimensions are connected in series. If and are the conductivities of the metal wires respectively, the effective conductivity if the combination is: (1) (2) (3) (4)
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: (1) \frac{\sigma_{1} \sigma_{z}}{\sigma_{1}+\sigma_{z}} (2) \frac{2 \sigma_{1} \sigma_{2}}{\sigma_{1}+\sigma_{2}} (3) \frac{\sigma_{1}+\sigma_{2}}{2 \sigma_{1} \sigma_{2}} (4) \frac{\sigma_{1}+\sigma_{z}}{\sigma_{1} \sigma_{2}}
Physics | Physics
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: (1) \frac{\sigma_{1} \sigma_{z}}{\sigma_{1}+\sigma_{z}} (2) \frac{2 \sigma_{1} \sigma_{2}}{\sigma_{1}+\sigma_{2}} (3) \frac{\sigma_{1}+\sigma_{2}}{2 \sigma_{1} \sigma_{2}} (4) \frac{\sigma_{1}+\sigma_{z}}{\sigma_{1} \sigma_{2}}

The Solution is (2)
\mathrm{R}_{\mathrm{ec}}=\frac{\ell}{\sigma_{1} \mathrm{~A}}+\frac{\ell}{\sigma_{1} \mathrm{~A}}=\frac{\ell_{\mathrm{eq}}}{\sigma_{\mathrm{eq}} \mathrm{A}_{\mathrm{eq}}}
\frac{2 \ell}{\sigma_{\mathrm{eq}} \mathrm{A}}=\frac{\ell}{\mathrm{A}}\left(\frac{\sigma_{1}+\sigma_{2}}{\sigma_{1} \sigma_{2}}\right)
\sigma_{\text {eq }}=\frac{2 \sigma_{1} \sigma_{2}}{\sigma_{1} \sigma_{2}}

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