Two batteries,one with an $emf$ of $3\,V$ and internal resistance $1\,\Omega$,and the other with an $emf$ of $15\,V$ and internal resistance $2\,\Omega$,are connected in series with a resistance $R$ as shown in the figure. If the potential difference between points $a$ and $b$ is zero,find the resistance $R$ in $\Omega$.

State the principle of a Wheatstone bridge.

Find the value of current $i_1$ for the circuit shown in the figure. (in $, A$)

The value of $I$ in the figure shown below is: (in $\text{ A}$)

If ${V_{AB}} = 4\,V$ in the given figure,then resistance $X$ will be .............. $\Omega$.

The resistances of the four arms $P, Q, R$ and $S$ in a Wheatstone's bridge are $10 \, \Omega$, $30 \, \Omega$, $30 \, \Omega$ and $90 \, \Omega$, respectively. The e.m.f. and internal resistance of the cell are $7 \, V$ and $5 \, \Omega$ respectively. If the galvanometer resistance is $50 \, \Omega$, the current drawn from the cell will be ............... $A$.