Q125 / 170 · Manipal (MET) 2017 · Physics

Two identical cells whether connected in parallel or in series gives the same current when connected to an external resistance $1.5 \Omega$. Find the value of internal resistance of each cell

  • A
    $1 \Omega$
  • B
    $0.5 \Omega$
  • C
    zero
  • Correct answer
    D
    $1.5 \Omega$

Solution

Let $n$ cells be in series and $m$ in parallel, then $\frac{n E}{R+n r}=\frac{E}{R+\frac{r}{m}}$ $\Rightarrow n\left[R+\frac{r}{m}\right]=R+n r$ $\Rightarrow n R m+n r=R m+m n r$ $\Rightarrow 6+2 r=3+4 r$ $\Rightarrow 2 r=3$ $\Rightarrow R=1.5 \Omega$

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

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