Question

You are provided with $48$ cells, each of emf $2$ volt and internal resistance $4$ ohms. What maximum current can flow in the circuit having an external resistance of $12\Omega$?

• A. $1A$
• B. $1.2A$
• C. $0.96A$
• D. $1.08A$

Answer 1

The correct option is A $1A$

Given : $E=2V$ $r=4\Omega$ $R=12\Omega$

Let there are $m$ cells in one row and there are $m$ such rows i.e $mn=48$ ...........(1)

For maximum current to flow through resistor $R$, then $r_{eq}=R$ ........(2)

Equivalent resistance of each row $r_1=mr$

$\therefore$ Total equivalent resistance of the circuit $r_{eq}=\frac{mr}{n}$

$\therefore$ $\frac{m\times 4}{n}=12$ $⟹m=3n$

From (1), $3n\times n=48$ $⟹n=4$ and $m=12$

Net equivalent emf of the circuit $E_{eq}=\sum \frac{E_i}{r_i}\times r_{eq}$ where $i$ represents the row number

$E_{eq}=[\frac{24}{48}+\frac{24}{48}+\frac{24}{48}+\frac{24}{48}]12=24V$

$\therefore$ Current flows $I=\frac{E_{eq}}{r_{eq}+R}=\frac{24}{12+12}=1A$