question_answer

The internal resistance of cell of emf 2 V is\[0.1\,\Omega .\] It is connected to a resistance of 3.9 \[\Omega .\] The voltage across the cell is:

A)  2.71 V                  

B)         1.95 V

C)  1.68 V                  

D)         0.52 V

Correct Answer: B

Solution :

Key Idea: The potential difference of a cell is less than the emf of the cell. When we connect the plates of a cell by a wire, an electric current flows in the wire from positive plate towards the negative plate. From law of conservation of energy.                 \[\text{work}\,\text{done}={{W}_{(external\,circuit)}}\]                 or            \[E\,i\,t=\,V\,i\,t+{{i}^{2}}r\,t\]                 \[\Rightarrow \]               \[V=E-ir\] \[\Rightarrow \]               \[V=E-\left( \frac{E}{R+r} \right)r\] Putting the numerical values, we have \[V=2-\left[ \frac{2}{3.9+0.1}\times 0.1 \right]\] \[=2-\frac{0.2}{4}\] \[=2-0.05=1.95\,V\]