Q73 / 75 · JEE Main 2020 (08 Jan Shift 2) · Physics

The series combination of two batteries, both of the same emf $10 V,$ but different internal resistance of $20 Ω$ and $5 Ω,$ is connected to the parallel combination of two resistors $30 Ω$ and $x Ω .$ The voltage difference across the battery of internal resistance $20 Ω$ is zero, the value of $x$ (in $Ω)$ is____

Correct answer: 30

Solution

$V_{1} = ϵ_{1} - i . r_{1}$
$0 = 10 - i \times 20$
$i = 0.5 A$
$V_{2} = \frac{7.5}{30} + \frac{7.5}{x}$
$0.5 = 0.25 + \frac{7.5}{x}$
$\frac{7.5}{x} = 0.25 x = \frac{7.5}{0.25} = 30 Ω$

Hence, the correct answer is 30.

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