Question

The $n$ row each containing $m$ cells in series are joined in parallel. Maximum current is taken from this combination across an external resistance of $3\Omega$ resistance. If the total number of cells used are $24$ 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

The correct option is C $m=12,n=2$

There are $n$ rows each containing $m$ cells means $m$ cells are connected in series. So, effective resistance of each branch will be

$r_{series}=mr$

Since total $n$ rows are present in mixed combination, so equivalent resistance of mixed combination will be

$r_{eq}=\frac{mr}{n}$

For maximum current in the circuit, external resistance should be equal to net internal resistance. So,

$R=\frac{mr}{n}$

$\because R=3\Omega ,r=0.5\Omega$

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

$\therefore m=6n....\left(1\right)$

And given that

$m\times n=24$

$\Rightarrow 6n\times n=24\left(\text{from equation}\right(1\left)\right)$

$\therefore n=2$ and $m=12$

Hence, option $\left(c\right)$ is correct.