A) \[{{r}_{1}}+{{r}_{2}}\]
B) \[{{r}_{1}}-{{r}_{2}}\]
C) \[\frac{{{r}_{1}}+{{r}_{2}}}{2}\]
D) \[\frac{{{r}_{1}}-{{r}_{2}}}{2}\]
Correct Answer: B
Solution :
Let the voltage across any one cell is V, then \[V=E-ir=E-{{r}_{1}}\,\left( \frac{2E}{{{r}_{1}}+{{r}_{2}}+R} \right)\] But V = 0 Þ \[E-\frac{2E{{r}_{1}}}{{{r}_{1}}+{{r}_{2}}+R}=0\] Þ \[{{r}_{1}}+{{r}_{2}}+R=2{{r}_{1}}\] Þ \[R={{r}_{1}}-{{r}_{2}}\]You need to login to perform this action.
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