A Copper (Cu) rod of length 25cm and cross – sectional area 3 mm² is joined with a similar aluminium (Al) rod as shown in figure. Find the resistance of the combination between the ends A and B.

(Take Resistivity of Copper = 1.7 * 10^-⁸ $Ω m$

Resistivity of Aluminium = 2.6 * 10^-⁸ $Ω m$ )

Option 1 - 0.858 <math><mrow></mrow></math> <math> <mrow> <mi>m</mi> <mi>Ω</mi> </mrow> </math>

Option 2 - 0.0858 <math> <mrow> <mi>m</mi> <mi>Ω</mi> </mrow> </math> <math><mrow></mrow></math>

Option 3 - 1.420 <math> <mrow> <mi>m</mi> <mi>Ω</mi> </mrow> </math>

Option 4 - 2.170   <math> <mrow> <mi>m</mi> <mi>Ω</mi> </mrow> </math>

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Vishal Baghel | Contributor-Level 10

6 months ago

Correct Option - 1

Detailed Solution:

$R_{1} = ?_{1} \frac{l}{A} R_{2} = ?_{2} \frac{l}{A}$

$\frac{1}{R} = \frac{1}{R_{1}} + \frac{1}{R_{2}} = \frac{A}{l} [\frac{1}{?_{1}} + \frac{1}{?_{2}}]$

$= \frac{3 * 1 0^{? 6}}{\frac{1}{4}} [\frac{1}{1.7 * 1 0^{? 8}} + \frac{1}{2.6 * 1 0^{? 8}}]$

$R = 0.858 * 1 0^{? 3} ?$

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A Copper (Cu) rod of length 25cm and cross – sectional area 3 mm2 is joined with a similar aluminium (Al) rod as shown in figure. Find the resistance of the combination between the ends A and B. (Take Resistivity of Copper = 1.7 * 10-8 Ω m Resistivity of Aluminium = 2.6 * 10-8 Ω m )

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