Q. Two wires of the same dimensions but resistivities $\rho_{1}$ and $\rho_{2}$are connected in series. The equivalent resistivity of the combination is
A) $\frac{\rho_{1} + \rho_{2}}{2}$
B) $\rho_{1} + \rho_{2}$
C) $2(\rho_{1} + \rho_{2})$
D) $\sqrt{\rho_{1}\rho_{2}}$
Explanation
(a) The effective resistance of combined wire
$\rho\left( \frac{l + l}{A} \right) = \frac{\rho_{1}l}{A} + \frac{\rho_{2}l}{A}\ $
(∵total length L=$l + l$)
Or
$\rho = \frac{\rho_{1} + \rho_{2}}{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.