Question

Two cells of internal resistances $r_1$ and $r_2$ and of same emf are connected in series, across a resistor of resistance R. If the terminal potential difference across the cells of internal resistance $r_1$ is zero, then the value of R is

• A. $R = 2 (r_1 + r_2)$
• B. $R = r_2 - r_1$
• C. $R = r_1 - r_2$
• D. $R = 2 (r_1 - r_2)$

Answer 1

Answer: (C)

$R = r_1 - r_2$

Answer 2

Current in the circuit : $I =\frac{2 E }{ R + r _{1}+ r _{2}}$ Terminal p.d. across $1^{\text {st }}$ cell is $V _{1}= E - Ir _{1}$ Given: $V _{1}=0$ $\Rightarrow E - Ir _{1}=0$ $E-\left(\frac{2 E}{R+r_{1}+r_{2}}\right) r_{1}=0$ $E =\frac{2 Er _{1}}{ R + r _{1}+ r _{2}}$ $R + r _{1}+ r _{2}=2 r _{1}$ or $R = r _{1}- r _{2}$