question_answer

Two identical batteries, each of emf \[2\,\,V\] and internal resistance \[1\Omega \] pass a current through external, resistance\[R=0.5\Omega \]. The maximum power that can be developed across \[R\] using these batteries is:

A) \[3.2\,\,W\]                       

B)  \[8.2\,\,W\]

C)  \[4\,\,W\]                                         

D)  \[2\,\,W\]

Correct Answer: D

Solution :

Key Idea: In parallel combination positive poles of all cells are connected to one point and negative poles to another point. The resistances of in are connected in parallel hence, equivalent resistance of combination is                 \[{{r}_{eq}}=\frac{1\times 1}{1+1}=0.5\] From Ohm?s law                 \[E=i(R+r)\] \[\therefore \]  \[i=\frac{2}{0.5+0.5}=2\,\,A\] Power is given by                 \[P={{i}^{2}}R={{(2)}^{2}}\times 0.5=2W\]