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  4. Two wires of same dimensions but resistivities ρ1 and ρ2 are connected in series. The equivalent resistivity of the combination is

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Q. Two wires of same dimensions but resistivities $\rho_1$ and $\rho_2$ are connected in series. The equivalent resistivity of the combination is

KCETKCET 2003Current Electricity

Solution:

$R _{1}=\frac{\rho_{1} l }{ A } R _{2}=\frac{\rho_{2} l }{ A } R + R =\frac{2 \rho l }{ A } \\ \therefore 2 R = R _{1}+ R _{2} \\ 2 \rho=\rho_{1}+\rho_{2} \quad \therefore \rho=\frac{1}{2}\left(\rho_{1}+\rho_{2}\right)$