Two cells of emfs E_1 and E_2 and internal resistances r_1 and r_2 are connected in parallel. The emf and internal resistance of the equivalent

Q: Two cells of $emfs$ $E_1$ and $E_2$ and internal resistances $r_1$ and $r_2$ are connected in parallel. The $emf$ and internal resistance of the equivalent source is

c In parallel connection ${{\rm{E}}_{{\rm{eq}}}} = \frac{{\Sigma \frac{{{{\rm{E}}_1}}}{{{{\rm{r}}_1}}}}}{{\Sigma \frac{1}{{{{\rm{r}}_1}}}}} \Rightarrow \frac{{\frac{{{{\rm{E}}_1}}}{{{{\rm{r}}_1}}} + \frac{{{{\rm{E}}_2}}}{{{{\rm{r}}_2}}}}}{{\frac{1}{{{{\rm{r}}_1}}} + \frac{1}{{{{\rm{r}}_2}}}}}{{\rm{E}}_{{\rm{eq}}}} = \frac{{{{\rm{E}}_1}{{\rm{r}}_2} + {{\rm{E}}_{2{\rm{r}}}}}}{{{{\rm{r}}_1} + {{\rm{r}}_2}}}$ $\frac{1}{{{r_{eq}}}} = \Sigma \frac{1}{{{r_1}}} = \frac{1}{{{r_1}}} + \frac{1}{{{r_2}}} \Rightarrow {r_{eq}} = \frac{{{r_1}{r_2}}}{{{r_1} + {r_2}}}$

SECTION - A [PHYSICS MCQ]

GSEB - English Medium

Two cells of $emfs$ $E_1$ and $E_2$ and internal resistances $r_1$ and $r_2$ are connected in parallel. The $emf$ and internal resistance of the equivalent source is

A${E_1}\, + \,{E_2}$ and $\frac{{{r_1}{r_2}}}{{{r_1} + {r_2}}}$
B${E_1}\, - \,{E_2}$ and $r_1\, +\, r_2$
C$\frac{{{E_1}{r_2}\, + \,\,{E_2}{r_1}}}{{{r_1} + {r_2}}}$ and $\frac{{{r_1}{r_2}}}{{{r_1} + {r_2}}}$
D$\frac{{{E_1}{r_2}\, + \,\,{E_2}{r_1}}}{{{r_1} + {r_2}}}$ and $r_1\, +\, r_2$

Medium

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

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