Question

A student while performing an experiment was surprised to find that when two identical cells are either connected in series or in parallel across a $2\Omega$ resistor, the same current passes through the resistor. What is the internal resistance of each cell?

• A. $2\Omega$
• B. $4\Omega$
• C. $1\Omega$
• D. $3\Omega$

Answer 1

The correct option is A $2\Omega$

In series , net $ϵ=nϵ$

net $r=nr$

Current =$\frac{n\epsilon }{nr+R}\to \left(1\right)$

In parallel , net $\epsilon$ = $\epsilon$ (in parallel $\epsilon$ is same)

net r $\frac{r}{n}$

Current =$\frac{\epsilon }{\frac{r}{n}+R}\to \left(2\right)$

According to question $n = 2 ,R = 2$

$\left(1\right)=\left(2\right)$

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

$r+4=2r+2$

r = 2$\Omega$