Infinite number of cells having emf and internal resistance left( {E,r} right), left( {frac{E}{n},frac{r}{n}} right), left( {frac{E}{{{n^2}}},frac{r}{{{n^2}}}} right), left( {frac{E}{{{n^3}}},frac{r}{{{n^3}}}} right)..... are connected in series

Q: Infinite number of cells having $emf$ and internal resistance $\left( {E,r} \right)$, $\left( {\frac{E}{n},\frac{r}{n}} \right)$, $\left( {\frac{E}{{{n^2}}},\frac{r}{{{n^2}}}} \right)$, $\left( {\frac{E}{{{n^3}}},\frac{r}{{{n^3}}}} \right)$..... are connected in series in same manner across an external resistance of $\frac{{nr}}{{n + 1}}$ . Current flowing through the external resistor is

d $I=\frac{E+\frac{E}{n}+\frac{E}{n^{2}}+\frac{E}{n^{3}} \ldots \ldots}{\left(r+\frac{r}{n}+\frac{r}{n^{2}}+\frac{r}{n^{3}}+\ldots\right)+\frac{n r}{n+1}}$ $\frac{{E\left[ {\frac{1}{{1 - \frac{1}{n}}}} \right]}}{{r\left[ {\frac{1}{{1 - \frac{1}{n}}}} \right] + \frac{{nr}}{{n + 1}}}}$ $\mathrm{I}=\frac{\frac{\mathrm{nE}}{(\mathrm{n}-1)}}{\frac{\mathrm{m}}{\mathrm{n}-1}+\frac{\mathrm{nr}}{\mathrm{n}+1}}=\mathrm{I}=\frac{\frac{\mathrm{E}}{(\mathrm{n}-1)}}{\left(\frac{\mathrm{n}+1+\mathrm{n}-1}{(\mathrm{n}-1)(\mathrm{n}+1)}\right) \mathrm{r}}$ $=\frac{(n+1) E}{2 n r}$

SECTION - A [PHYSICS MCQ]

GSEB - English Medium

Infinite number of cells having $emf$ and internal resistance $\left( {E,r} \right)$, $\left( {\frac{E}{n},\frac{r}{n}} \right)$, $\left( {\frac{E}{{{n^2}}},\frac{r}{{{n^2}}}} \right)$, $\left( {\frac{E}{{{n^3}}},\frac{r}{{{n^3}}}} \right)$..... are connected in series in same manner across an external resistance of $\frac{{nr}}{{n + 1}}$ . Current flowing through the external resistor is

A$\frac{E}{{2r}}$
B$\frac{E}{{\left( {n - 1} \right)r}}$
C$\frac{{\left( {n - 1} \right)E}}{{2n}}$
D$\frac{{\left( {n + 1} \right)E}}{{2nr}}$

Diffcult

STD 11 Science
JEE
STD 12 - 3. current electricity
Physics

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