A) \[R={{r}_{1}}+{{r}_{2}}\]
B) \[R=\frac{{{r}_{1}}}{{{r}_{2}}}\]
C) \[R={{r}_{1}}-{{r}_{2}}\]
D) \[R=\frac{{{r}_{2}}}{{{r}_{1}}}\]
Correct Answer: C
Solution :
The total emf = E + E = 2E Total resistance \[=R+{{r}_{1}}+{{r}_{2}}\] \[\therefore \]Current flowing through the circuit \[i=\frac{2E}{R+{{r}_{1}}+{{r}_{2}}}\] According to question \[E=i{{r}_{1}}\Rightarrow i=\frac{E}{{{r}_{1}}}\] \[\therefore \] \[\frac{E}{{{r}_{1}}}=\frac{2E}{R+{{r}_{1}}+{{r}_{2}}}\]
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