Question

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

• A. $2(\rho_1 + \rho_2)$
• B. $\sqrt{\rho_1\rho_2}$
• C. $\frac{\rho_1+\rho_2}{2}$
• D. $1/2(\rho_1+\rho_2)$

Answer 1

Answer: (D)

$1/2(\rho_1+\rho_2)$

Answer 2

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