| Two batteries of emf \[{{\varepsilon }_{1}}\] and \[{{\varepsilon }_{2}}\] \[({{\varepsilon }_{2}}>{{\varepsilon }_{1}})\] and internal resistances \[{{r}_{1}}\] and \[{{r}_{2}}\] respectively are connected in parallel as shown in figure : |
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A) The equivalent emf \[{{\varepsilon }_{\operatorname{eq}}}\] of the two cells is between \[{{\varepsilon }_{1}}\] and \[{{\varepsilon }_{2}},\ i.e.{{\varepsilon }_{1}}<{{\varepsilon }_{\operatorname{eq}}}<{{\varepsilon }_{2}}\]
B) The equivalent emf \[{{\varepsilon }_{\operatorname{eq}}}\] is smaller than \[{{\varepsilon }_{1}}\].
C) The \[{{\varepsilon }_{\operatorname{eq}}}\] is given by \[{{\varepsilon }_{\operatorname{eq}}}\]=\[{{\varepsilon }_{1}}\]+ \[{{\varepsilon }_{2}}\] always.
D) \[{{\varepsilon }_{\operatorname{eq}}}\] is independent of internal resistances \[{{r}_{1}}\] and \[{{r}_{2}}\]
Correct Answer: A
Solution :
| Option [a] is correct |
| Explanation: As we know that the equivalent emf in parallel combination of cells is: |
| \[{{\varepsilon }_{\operatorname{eq}}}=\ \frac{({{\varepsilon }_{1}}{{r}_{2}}+{{\varepsilon }_{2}}{{r}_{1}})}{({{r}_{1}}+{{r}_{2}})}\] |
| so, it is clear that part 'c' and '& are incorrect by formula. According to this formula only option (A), is correct. |
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