In an aluminium $(A1)$ bar of square cross section, a square hole is drilled and is filled with iron ( $Fe$ ) as shown in the figure. The electrical resistivities of $A 1$ and $Fe$ are $2.7 \times 10^{-8} \ \Omega m$ and $1.0 \times 10^{-7} \ \Omega m$, respectively. The electrical resistance between the two faces $P$ and $Q$ of the composite bar is
IIT 2015, Advanced
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$R_{ F }=\frac{\rho_{ F } \times 50 \times 10^{-3}}{\left(2 \times 10^{-3}\right)^2}=1250 \mu \Omega $
$R_{A l}=\frac{\rho_{A \ell} \times 50 \times 10^{-3}}{(49-4) \times 10^{-6}}=30 \mu \Omega $
$R_{* q}=\frac{1250 \times 30}{1280}=\frac{1875}{64} \mu \Omega$
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