The rod given in the figure is made of two different materials. Both have square cross-section of side 3mm. The resistivity of the first material is $4 x 10^{- 3} Ω - m$ and it is 25cm long while that of the second material is $5 x 10^{- 3} Ω - m$ and is of length 70cm. The equivalent resistivity of the rod between its ends is __________ $\times 10^{- 3} Ω - m$ (roundoff to nearest integer)

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answer is 4.74.

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Detailed Solution

$ρ_{eq} = \frac{ρ_{1} l_{1} + ρ_{2} l_{2}}{l_{1} + l_{2}}$

$\Rightarrow ρ_{eq} = \frac{4 x 10^{- 3} . 25 + 5 x 10^{- 3} . 70}{25 + 70} = 4.74 x 10^{- 3} Ω - m ≃ 5 x 10^{- 3} Ω - m$

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