A) \[\frac{{{I}_{1}}{{R}_{1}}+{{I}_{2}}{{R}_{2}}}{{{I}_{1}}+{{I}_{2}}}\]
B) \[\frac{{{I}_{1}}{{R}_{2}}+{{I}_{2}}{{R}_{1}}}{{{I}_{1}}+{{I}_{2}}}\]
C) \[\frac{{{I}_{1}}{{R}_{2}}+{{I}_{2}}{{R}_{1}}}{{{I}_{1}}-{{I}_{2}}}\]
D) \[\frac{{{I}_{2}}{{R}_{2}}+{{I}_{1}}{{R}_{1}}}{{{I}_{1}}-{{I}_{2}}}\]
Correct Answer: D
Solution :
\[{{\operatorname{I}}_{1}}=\frac{E}{r+{{R}_{1}}}{{\operatorname{I}}_{2}}=\frac{E}{r+{{R}_{2}}}\] \[\frac{{{\operatorname{I}}_{1}}}{{{\operatorname{I}}_{2}}}=\frac{r+{{R}_{2}}}{r+{{R}_{1}}}\] \[{{\operatorname{I}}_{1}}r+{{I}_{1}}{{R}_{1}}={{\operatorname{I}}_{2}}r+{{I}_{2}}{{R}_{2}}\] \[r\left( {{\operatorname{I}}_{1}}-{{I}_{2}} \right)={{I}_{2}}{{R}_{2}}-{{I}_{1}}{{R}_{1}}\] \[r=\frac{{{I}_{2}}{{R}_{2}}-{{I}_{1}}{{R}_{1}}}{{{\operatorname{I}}_{1}}-{{\operatorname{I}}_{2}}}\]You need to login to perform this action.
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