Question

$N$ identical cells are connected to form a battery. When the terminals of the battery are joined directly (short-circuited), current $I$ flows in the circuit. To obtain the maximum value of $I,$

• A. all the cells should be joined in series
• B. all the cells should be joined in parallel
• C. two rows of $N/2$ cells each should be joined in parallel
• D. $\sqrt{N}$ rows of $\sqrt{N}$ cells each should be joined in parallel, given that $\sqrt{N}$ is an integer

Answer 1

The correct option is B all the cells should be joined in parallel

Let emf of each cell $=\epsilon$ and internal resistance $=r$
When all cell is joined in series: net resistance $r_t=Nr$ and total emf ${\epsilon }_t=N\epsilon$
thus,current , $I_S=\frac{{\epsilon }_t}{r_t}=\frac{N\epsilon }{Nr}=\frac{\epsilon }{r}$
When all cell is joined in parallel: net resistance $r_t=r/N$ and total emf ${\epsilon }_t=\epsilon$
thus,current , $I_P=\frac{{\epsilon }_t}{r_t}=\frac{\epsilon }{r/N}=\frac{N\epsilon }{r}$
Thus current $I_P$ is maximum.