JEE Main 2026 Jan 28 Shift 1, Physics Q13: Kirchhoff’s Laws

JEE Main2026Jan 28, Shift 1Physics

For the two cells having same EMF E and internal resistance $r$ , the current passing through the external resistor 6 $Ω$ is same when both the cells are connected either in parallel or in series. The value of internal resistance $r$ is ______ $Ω$ .

Solution

Two identical cells (EMF $E$ , internal resistance $r$ ) with external $R = 6 Ω$ :

Series: EMFs add ( $2 E$ ), internal resistances add ( $2 r$ ): $i_{s} = \frac{2 E}{6 + 2 r}$ .

Parallel: EMF $= E$ , internal $= r /2$ : $i_{p} = \frac{E}{6 + r /2}$ .

Set $i_{s} = i_{p}$ :

$\frac{2 E}{6 + 2 r} = \frac{E}{6 + r /2}$

$2 (6 + r /2) = 6 + 2 r$

$12 + r = 6 + 2 r \Rightarrow r = 6 Ω$ .

Option (4).

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JEE Main 2026 Jan 28 Shift 1, Physics Q13: Kirchhoff’s Laws

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