Question

Two cells of emf $2 E$ and $E$ with internal resistance $r _{1}$ and $r _{2}$ respectively are connected in series to an extemal resistor $R$ (see figure). The value of $R$, at which the potential difference across the terminals of the first cell becomes zero is

• A. $r _{1}+ r _{2}$
• B. $\frac{r_{1}}{2}-r_{2}$
• C. $\frac{ r _{1}}{2}+ r _{2}$
• D. $r _{1}- r _{2}$

Answer 1

Answer: (B)

$i =\frac{3 E }{ R + r _{1}+ r _{2}}$
$TPD =2 E - ir _{1}=0$
$2 E = ir _{1}$
$2 E =\frac{3 E \times r _{1}}{ R + r _{1}+ r _{2}}$
$2 R +2 r _{1}+2 r _{2}=3 r _{1}$
$R =\frac{ r _{1}}{2}- r _{2}$