Q. The series combination of two batteries, both of the same emf $10\, V$, but different internal resistance of $20\,\Omega$ and $5\,\Omega$, is connected to the parallel combination of two resistors $30\,\Omega$ and $R\,\Omega$. The voltage difference across the battery of internal resistance $20\,\Omega$ is zero, the value of $R$ (in $\Omega$) is __________ .
Solution:
$E_{1}=E-ir\,E_{2}=E-ir$
$= 10 - i20 = 0\,= 10 - 0.5 × 5$
$i = 0.5\, A\,=7.5\,V$
$E_{net}=E_{1}+E_{2}=7.5\,V
i=i_{1}+i_{2}$
$0.5=\frac{7.5}{x}+\frac{7.5}{30}$
$x=30\,\Omega$
