Two identical cells gave the same current through an external resistance of $2 \Omega$ regardless whether the cells are grouped in series or parallel. The internal resistance of the cells is

• A

  $1 \Omega$
• B

  $0.5 \Omega$
• C

  $1.5 \Omega$
• Correct answer
  D

  $2.0 \Omega$

Solution

For first case, $I=\frac{2 E}{R+2 r}$...(i)

For second case, $I=\frac{E}{R+\frac{r}{2}}=\frac{2 E}{2 R+r}$....(ii)
From eqs(i) and (ii), we get $\mathrm{R}+2 \mathrm{r}=2 \mathrm{R}+\mathrm{r} \Rightarrow \mathrm{r}=\mathrm{R}=2 \Omega$

Hence, the correct answer is option: 'D'.