question_answer

In the following circuit,\[18\,\,\Omega \] resistor develops, 2 J/sec due to current flowing through it. The power developed across \[10\,\,\Omega \], resistance is

A) 125 W  

B)   10 W    

C) \[\frac{4}{5}\,\,W\]                   

D) 25 W

Correct Answer: B

Solution :

The given circuit can be redrawn as follows \[\frac{{{i}_{1}}}{{{i}_{2}}}=\frac{9}{18}=\frac{1}{2}\] and \[i={{i}_{1}}+{{i}_{2}}\] \[\Rightarrow \,\,\,\frac{i}{{{i}_{1}}}\,\,=\,\,1+\frac{{{i}_{2}}}{{{i}_{1}}}\,\,=\,\,1\,+\,2=3\] \[From\,\,P={{i}^{2}}R\,\,\Rightarrow \,\,\frac{{{P}_{10\Omega }}}{{{P}_{18\Omega }}}\,\,=\,\,\left( \frac{i}{{{i}_{1}}} \right){{\,}^{2}}\,\times \,\,\frac{10}{18}\] \[\Rightarrow \,\,\,{{P}_{10\,\Omega }}\,\,=\,\,10\,W\]