JEE MAIN - Physics (2023 - 31st January Morning Shift - No. 26)
Two identical cells, when connected either in parallel or in series gives same current in an external resistance $$5 ~\Omega$$. The internal resistance of each cell will be ___________ $$\Omega$$.
Answer
5
Explanation
_31st_January_Morning_Shift_en_26_1.png)
$\varepsilon_{\text {series }}=\varepsilon_{1}+\varepsilon_{2}=2 \varepsilon$
$r_{\text {series }}=r_{1}+r_{2}=2 r$
$i=\frac{2 \varepsilon}{5+2 r}$ ......(1)
_31st_January_Morning_Shift_en_26_2.png)
$\varepsilon_{\text {parallel }}=\frac{\frac{\varepsilon_{1}}{r_{1}}+\frac{\varepsilon_{2}}{r_{2}}}{\frac{1}{r_{1}}+\frac{1}{r_{2}}}=\varepsilon$
$ r_{\text {parallel }}=\frac{r}{2}$
$$ i=\frac{\varepsilon}{\frac{r}{2}+5} $$ .......(2)
Equating (1) and (2), we get
$\Rightarrow \frac{2 \varepsilon}{2 r+5}=\frac{\varepsilon}{\frac{r}{2}+5}$
$\Rightarrow r+10=2 r+5 $
$\Rightarrow r=5 \Omega$
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