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  4. A dc source of emf E1 = 100 V and internal resistance r = 0.5 Ω, a storage battery of emf E2 = 90 V and an external resistance R are connected as shown in figure. For what value of R no current will pass through the battery ?

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Q. A dc source of emf $E_1 = 100 \,V$ and internal resistance $r = 0.5\, \Omega$, a storage battery of emf $E_2 = 90\, V$ and an external resistance $R$ are connected as shown in figure. For what value of $R$ no current will pass through the battery ?Physics Question Image

JEE MainJEE Main 2013Current Electricity

Solution:

$\frac{100}{R+r}= \frac{90}{R}$
$\Rightarrow \frac{R+r}{R}=\frac{10}{9}$
$\Rightarrow 1+\frac{0.5}{R}=\frac{10}{9}$
$\frac{0.5}{R}=\frac{1}{9}$
$\therefore R=4.5\,\Omega$