Question

The combination of two identical cells, whether connected in series or parallel combination provides the same current through an external resistance of $2\Omega$. The value of internal resistance of each cell is

• A. $4\Omega$
• B. $2\Omega$
• C. $8\Omega$
• D. $6\Omega$

Answer 1

The correct option is B $2\Omega$


From diagrams:

$i_{\text{parallel}}=\frac{E}{2+\frac{r}{2}}\text{and}{i}_{\text{series}}=\frac{2E}{2+2r}$

$\text{given}{i}_{\text{parallel}}=i_{\text{series}}$

$\frac{1}{2+\frac{r}{2}}=\frac{1}{1+r}$

$1+r=2+\frac{r}{2}$

$r=2\Omega$

Hence, $\left(A\right)$ is the correct answer.