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STD 12 - 3. current electricity — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 3. current electricity4 Marks
MCQ
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 internal resistance of cell is
  • A
    $\frac{(R+r)}{2}$
  • B
    $\frac{(R-r)}{2}$
  • C
    $\frac{(R r)}{2}$
  • ✓
    $\sqrt{(R r)}$
✓

Answer

Correct option: D.
$\sqrt{(R r)}$
d
(d)

$H_1=\frac{E^2 R}{\left(R+r_1\right)^2}$

$H_2=\frac{E^2 R}{\left(r+r_1\right)^2}$

$\frac{R}{\left(R+r_1\right)^2}=\frac{r}{\left(r+r_1\right)^2}$

$\frac{r+r_1}{R+r_1}=\frac{\sqrt{r}}{\sqrt{R}}$

$\sqrt{R} r_1+r \sqrt{R}=\sqrt{r} r_1+R \sqrt{r}$

$r_1(\sqrt{R}-\sqrt{r})=\sqrt{R r}(\sqrt{R}-\sqrt{r})$

$r_1=\sqrt{R r}$

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