Question 185 of 380

Five identical cells each of internal resistance $1\Omega$ and emf $5V$ are connected in series and in parallel with an external resistance $R.$ For what value of $R,$ current in series and parallel combination will remain the same?

A$1\Omega$B$5\Omega$C$25\Omega$D$10\Omega$

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Answer: (A) $1\Omega$

${i}_{1}=\dfrac{5\epsilon }{R+5r}...\left(1\right)$


${I}_{2}=\dfrac{\epsilon }{R+\dfrac{r}{5}}...\left(2\right)$
From equation $\left(1\right)$ and $\left(2\right)$
${i}_{1}={i}_{2}$
$\dfrac{5\epsilon }{R+5r}=\dfrac{\epsilon }{R+\dfrac{r}{5}}\Rightarrow R=r=1\Omega$