Question

A cell sends a current through a resistance $R$ for time $t$. Now the same cell sends current through another resistance $r$ for the same time. If same amount of heat is developed in both the resistance, then the intemal resistance of cell is

• A. $\frac{(R+r)}{2}$
• B. $\frac{(R-r)}{2}$
• C. $\frac{(Rr)}{2}$
• D. $\sqrt{(Rr)}$

Answer 1

Answer: (D)

$H_1=\frac{E^{2}R}{{\left(R+r_1\right)}^2}$
$H_2=\frac{E^{2}R}{{\left(r+r_1\right)}^2}$
$\frac{R}{{\left(R+r_1\right)}^2}=\frac{r}{{\left(r+r_1\right)}^2}$
$\frac{r+r_1}{R+r_1}=\frac{\sqrt{r}}{\sqrt{R}}$
$\sqrt{R}{r}_1+r\sqrt{R}$
$=\sqrt{r}{r}_1+R\sqrt{r}$
$r_1(\sqrt{R}-\sqrt{r})$
$=\sqrt{Rr}(\sqrt{R}-\sqrt{r})$
$r_1=\sqrt{Rr}$