A) \[1\,\Omega \]
B) \[2\,\Omega \]
C) \[3\,\Omega \]
D) \[4\,\Omega \]
Correct Answer: B
Solution :
Current in external circuit when the cells are in series combination \[{{i}_{1}}=\frac{{{E}_{1}}+{{E}_{2}}}{R+{{r}_{1}}+{{r}_{2}}}=\frac{E+E}{2+r+r}=\frac{E}{1+r}\] Similarly, when the cells are in parallel combination, \[{{i}_{2}}=\frac{{{E}_{1}}}{R+{{r}_{1}}/2}=\frac{E}{2+r/2}=\frac{2E}{4+r}\] but \[{{i}_{1}}={{i}_{2}}\](given) \[\therefore \] \[\frac{E}{1+t}=\frac{2E}{4+r}\] or \[2+2r=4+r\] \[\therefore \] \[r=2\Omega \]
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