Question

If the potential difference across the internal resistance $r_1$ is equal to the emf $E$ of the battery, then

• A. $R = r_1 +r_2$
• B. $R = \frac{r_1}{r_2}$
• C. $R = r_1 -r_2$
• D. $R = \frac{r_2}{r_1}$

Answer 1

Answer: (C)

$R = r_1 -r_2$

Answer 2

The total $emf =E+E=2 E$
Total resistance $=R+r_{1}+r_{2}$
$\therefore$ Current flowing through the circuit
$i=\frac{2 E}{R+r_{1}+r_{2}}$
According to question $E=i r_{1}$
$\Rightarrow \, i=\frac{E}{r_{1}}$
$\therefore\, \frac{E}{r_{1}}=\frac{2 E}{R+r_{1}+r_{2}}$
$R=r_{1}-r_{2}$