Q63 / 90 · JEE Main 2021 (27 Aug Shift 1) · Physics

Five identical cells each of internal resistance $1 Ω$ and emf $5 V$ 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?

Solution

$i_{1} = \frac{5 ε}{R + 5 r} . . . (1)$

$I_{2} = \frac{ε}{R + \frac{r}{5}} . . . (2)$

From equation $(1)$ and $(2)$

$i_{1} = i_{2}$

$\frac{5 ε}{R + 5 r} = \frac{ε}{R + \frac{r}{5}} \Rightarrow R = r = 1 Ω$

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