Q. Two cells with the same emf E and different internal resistances $r_{1}$and $r_{2}$ are connected in series to an external resistance R. the value of R so that the potential difference across the first cell be zero is
A) $\sqrt{r_{1}r_{2}}$
B) $r_{1} + r_{2}$
C) $r_{1} - r_{2}$
D) $\frac{r_{1} + r_{2}}{2}$
Explanation
(c) $I = \frac{2E}{R + r_{1} + r_{2}}$
Potential difference across first cell
$V = E - Ir_{1} = 0$
$E - \frac{2{Er}_{1}}{R + r_{1} + r_{2}} = 0$
$\left\lbrack \frac{R + r_{1} + r_{2} - 2r_{1}}{R + r_{1} + r_{2}} \right\rbrack = 0$
$\Longrightarrow \ \ \ R + r_{2} - r_{1} = 0\ $
$\Longrightarrow \ \ R = r_{1} - r_{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.