The series combination of two batteries, both of the same emf $10 \mathrm{~V}$, but different internal resistance of $20 \Omega$ and $5 \Omega$, is connected to the parallel combination of two resistors $30 \Omega$ and $\mathrm{R} \Omega$. The voltage difference across the battery of internal resistance $20 \Omega$ is zero, the value of $R$ (in $\Omega$ ) is _______
The resistance of $30 \Omega$ is in parallel with $R$. Their effective resistance
$\frac{1}{R^{\prime}}=\frac{1}{30}+\frac{1}{R}$
$R^{\prime}=\frac{30 R}{30+R}$ ....(1)
Also, V $=\mathrm{IR}$
$\Rightarrow 10=\frac{20 \times 20}{R^{\prime}+25}$
$\Rightarrow R^{\prime}+25=40$
$\Rightarrow R^{\prime}=15$
$R^{\prime}=15=\frac{30 R}{30+R}$ Using (i)
$\Rightarrow 30+R=2 R$
$\Rightarrow R=30 \Omega$
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