Q. Two wires of same dimensions but resistivities $\rho_{1}$ and $\rho_{2}$are connected in series. The equivalent resistivity of the combination is
A) $\sqrt{\rho_{1}\rho_{2}}$
B) $(\rho_{1} + \rho_{2})$
C) $\frac{\rho_{1} + \rho_{2}}{2}$
D) None of these
Explanation
(c) $R = R_{1} + R_{2} = \frac{\rho_{1}l}{A} + \frac{\rho_{2}l}{A} = \left( \rho_{1} + \rho_{2} \right)\frac{l}{A}$ …(i)
$R = \frac{\rho(2l)}{A}$ …(ii)
From Eqs.(i) and (ii), $2\rho = \rho_{1} + \rho_{2}\ or\ \rho = \frac{\rho_{1} + \rho_{2}}{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.