Given below are two statements :Statement-I : | vedclass

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(D) For two batteries with emfs $\varepsilon_1, \varepsilon_2$ and internal resistances $r_1, r_2$ connected in parallel,the equivalent emf $\varepsil

Vedclass · Accepted Answer

Statement-$I$ is false but Statement-$II$ is true

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(D) For two batteries with emfs $\varepsilon_1, \varepsilon_2$ and internal resistances $r_1, r_2$ connected in parallel,the equivalent emf $\varepsilon_{eq}$ is given by $\varepsilon_{eq} = \frac{\frac{\varepsilon_1}{r_1} + \frac{\varepsilon_2}{r_2}}{\frac{1}{r_1} + \frac{1}{r_2}}$.This value of $\varepsilon_{eq}$ always lies between $\varepsilon_1$ and $\varepsilon_2$. Thus,Statement-$I$ is false because it is not necessarily smaller than both.The equivalent internal resistance $r_{eq}$ is given by $\frac{1}{r_{eq}} = \frac{1}{r_1} + \frac{1}{r_2}$,which implies $r_{eq} = \frac{r_1 r_2}{r_1 + r_2}$.Since $r_{eq} = \frac{r_1 r_2}{r_1 + r_2}$,it is clear that $r_{eq} < r_1$ and $r_{eq} < r_2$. Thus,Statement-$II$ is true.

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