Question

The series combination of two batteries, both of the same emf $10V,$ 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......

Answer 1

$V_{1}=\epsilon _{1}-i\cdot r_{1}$
$0=10-i\times 20$
$i=0.5A$
$V_{2}=\epsilon _{2}-ir_{2}$
$=10-0.5\times 5$
$V_{2}=7.5V$
$0.5=\frac{7 . 5}{30}+\frac{7 . 5}{x}$
$0.5=0.25+\frac{7 . 5}{x}$
$\frac{7 . 5}{x}=0.25$
$x=\frac{7 . 5}{0 . 25}=30$