For which value of resistance $R$ does the galvanometer show zero deflection in the electrical circuit shown below (in $\Omega$)?

The resistance of a voltameter is $2\,\Omega$. It is connected in series to a battery of $10\,V$ through a resistance of $3\,\Omega$. In a certain time,the mass deposited on the cathode is $1\,g$. Now,the voltameter and the $3\,\Omega$ resistance are connected in parallel with the battery. The increase in the deposited mass on the cathode in the same time will be .............. $g$.

The currents $i_1$ and $i_2$ through the resistors $R_1 (= 10\,\Omega)$ and $R_2 (= 30\,\Omega)$ in the circuit diagram with $E_1 = 3\,V, E_2 = 3\,V$ and $E_3 = 2\,V$ are respectively:

What is the current $i$ in the circuit as shown in the figure (in $A$)?

One end each of a resistance $r$,a capacitor $C$,and a resistance $2r$ are connected together. The other ends are respectively connected to the positive terminals of batteries $P$,$Q$,and $R$ having emfs $E$,$E$,and $2E$. The negative terminals of the batteries are then connected together. In this circuit,with steady current,the potential drop across the capacitor is:

Which of the following acts as a circuit protection device?