A) The equivalent emf E is smaller than \[{{E}_{1}}\]
B) The equivalent emf \[\operatorname{E} = {{E}_{1}} + {{E}_{2}}\]
C) The equivalent emf E is smaller than \[{{E}_{1}}\]
D) The equivalent emf \[{{E}_{eq}}\] of two cell is between \[{{E}_{1}}\,\,and\,\,{{E}_{2}}\] always
Correct Answer: D
Solution :
The equivalent internal resistance of two cells between A and B /en = \[{{r}_{eq}}=\frac{{{r}_{1}}{{r}_{2}}}{{{r}_{1}}+{{r}_{2}}}\] (Parallel combination case of resistances) If E is the equivalent emf of the two cells in parallel between A and B, then \[\frac{{{E}_{eq}}}{{{r}_{eq}}}=\frac{{{E}_{1}}}{{{r}_{1}}}=\frac{{{E}_{2}}}{{{r}_{2}}}=\frac{{{E}_{1}}\,{{r}_{2}}+{{E}_{2}}\,{{r}_{1}}}{{{r}_{1}}\,{{r}_{2}}}\] \[\therefore \,\,\,\,\,\,\,\,\,\,{{E}_{eq}}=\frac{{{E}_{1}}\,{{r}_{2}}+{{E}_{2}}\,{{r}_{1}}}{{{r}_{1}}\,{{r}_{2}}}{{r}_{eq}}=\frac{{{E}_{1}}\,{{r}_{2}}+{{E}_{2}}\,{{r}_{1}}}{({{r}_{1}}+{{r}_{2}})}\] As \[{{E}_{2}}>{{E}_{1}}\,\,\,\Rightarrow \,\,\,{{E}_{1}}<E<{{E}_{2}}\,\] [For all values of \[{{r}_{1}}\,\,and\,\,{{r}_{2}}\]]
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