Question

When two identical cells are connected either in series or in parallel across 2 ohm resistor they send the same current through it. The internal resistance of each cell is :

• A. $2ohm$
• B. $1.2ohm$
• C. $12ohm$
• D. $21ohm$

Answer 1

Answer: (A)

$2ohm$

Let voltage of each cell is = $E$, internal resistance of each cell is = $r$

When cells are in series-

Effective voltage of circuit = $E+E=2E$

And effective resistance of circuit = $r+r+2=2(1+r)$

Current $I_1=\frac{E}{(1+r)}$

When cells are in parallel-

Effective voltage of circuit = $E$

Effective resistance of circuit = $r||r+2$ = $\frac{r}{2}+2=\frac{r+4}{2}$

Current $I_2=\frac{2E}{r+4}$

As $I_1=I_2$ $⟹$ $\frac{E}{(1+r)}=\frac{2E}{(r+4)}⟹r=2\Omega$