Question

The $n$ rows each containing in cells in series are joined in parallel. Maximum current is taken from this combination across an external resistance of $3\Omega$. If the total number of cells used is $24$ and internal resistance of each cell is $0.5\Omega$, then

• A. $m=8,n=3$
• B. $m=6,n=4$
• C. $m=12,n=2$
• D. $m=2,n=12$

Answer 1

Answer: (C)

$m=12,n=2$

Current is maximum when equivalent resistance is equal to external resistance of $3$ ohm.

Now total resistance is $\frac{m\times 0.5}{n}$. (Resistances are parallel so they are directly added to each other)

According to question:

$\frac{m\times 0.5}{n}=3$

$\Rightarrow \frac{m}{n}=6$

As ratio of $m$ and $n$ is 6,then best option which satisfy this relation is option C