Two batteries one of the $\mathrm{emf}$ $3\,V$, internal resistance $1$ ohm and the other of $\mathrm{emf}$ $15\, V$, internal resistance $2$ $\mathrm{ohm}$ are connected in series with a resistance $R$ as shown. If the potential difference between $a$ and $b$ is zero the resistance of $R$ in $\mathrm{ohm}$ is
Medium
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Let the current $I$ will flow in the anticlockwise direction.
By $KVL,$ $15+3=(1+2+R) I$ or $I=\frac{18}{3+R}$
Here, $V_{a b}=0$
or $3-1 I=0$
or $3=I=\frac{18}{3+R}$
or $R=3 \Omega$
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