Two metallic wires of identical… - JEE Main 2022 Physics PYQ

JEE Main 2022 — Physics Thermodynamics

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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 :

Official previous-year question

Held on 29 Jul 2022 · Verified 6 Jul 2026.

Options

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

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Solution

JEE Main 2022 Physics, Thermal Properties of Matter — solution figure

Let length of wire be $l$ ,

Area of wire as $A$

For equivalent wire length $=2l$ & area will be $A$

As the wires are connected in series combination, the thermal resistance

${R}_{eq}={R}_{1}+{R}_{2}$

$\Rightarrow \frac{2l}{{\sigma }_{\mathrm{eq}}A}=\frac{l}{{\sigma }_{1}A}+\frac{l}{{\sigma }_{1}A}$

$\Rightarrow \frac{2}{{\sigma }_{\mathrm{eq}}}=\frac{1}{{\sigma }_{1}}+\frac{1}{{\sigma }_{2}} \Rightarrow {\sigma }_{\mathrm{eq}}=\frac{2{\sigma }_{1}{\sigma }_{2}}{{\sigma }_{1}+{\sigma }_{2}}$

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Options

$\frac{{\sigma }_{1}{\sigma }_{2}}{{\sigma }_{1}+{\sigma }_{2}}$

$\frac{2{\sigma }_{1}{\sigma }_{2}}{{\sigma }_{1}+{\sigma }_{2}}$

$\frac{{\sigma }_{1}+{\sigma }_{2}}{2{\sigma }_{1}{\sigma }_{2}}$

$\frac{{\sigma }_{1}+{\sigma }_{2}}{{\sigma }_{1}{\sigma }_{2}}$

Solution

JEE Main 2022 Physics, Thermal Properties of Matter — solution figure

Let length of wire be $l$ ,

Area of wire as $A$

For equivalent wire length $=2l$ & area will be $A$

As the wires are connected in series combination, the thermal resistance

${R}_{eq}={R}_{1}+{R}_{2}$

$\Rightarrow \frac{2l}{{\sigma }_{\mathrm{eq}}A}=\frac{l}{{\sigma }_{1}A}+\frac{l}{{\sigma }_{1}A}$

$\Rightarrow \frac{2}{{\sigma }_{\mathrm{eq}}}=\frac{1}{{\sigma }_{1}}+\frac{1}{{\sigma }_{2}} \Rightarrow {\sigma }_{\mathrm{eq}}=\frac{2{\sigma }_{1}{\sigma }_{2}}{{\sigma }_{1}+{\sigma }_{2}}$

Options

Did you get this right?

Solution

Your note

JEE Main Thermodynamics in other years

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Options

Did you get this right?

Solution

Your note

JEE Main Thermodynamics in other years

More JEE Main Thermodynamics questions

Other Physics topics for JEE Main

Mechanics

Electromagnetism

Modern Physics

Optics

Waves & Oscillations

Keep practicing Thermodynamics