A Copper (Cu) rod of length 25 cm and cross-sectional area 3 mm2 is… | JEE Main 2021 (22 Jul, Shift 2)

Q48JEE Main 2021 · 22 JUL · SHIFT 2Medium

Combination of Resistors

A Copper (Cu) rod of length 25 cm 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 $\times$ 10 $-$ 8 $\Omega$ m and Resistivity of Aluminium = 2.6 $\times$ 10 $-$ 8 $\Omega$ m)

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Answer: (c)

The rods are in parallel. $R = \dfrac{\rho l}{A}$ with $l = 0.25$ m, $A = 3 \times 10^{-6}\ \text{m}^2$ .
$R_{Cu} = \dfrac{1.7 \times 10^{-8} \times 0.25}{3 \times 10^{-6}} = 1.417\ \text{m}\Omega$ , $R_{Al} = 2.167\ \text{m}\Omega$
$R_{AB} = \dfrac{1.417 \times 2.167}{1.417 + 2.167} \approx 0.858\ \text{m}\Omega$
So the answer is (c) $0.858\ \text{m}\Omega$ .

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Combination of Resistors question from JEE Main 2021 (22 Jul, Shift 2)

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