In the circuit shown in the figure reading of voltmeter is $V_1$ when only $S_1$ is closed, the reading of voltmeter is $V_2$ when only $S_2$ is closed and the reading of voltmeter is $V_3$ when both $S_1$ and $S_2$ are closed. Then:-

The potential difference through the $3 \mathrm{\Omega }$ resistor shown in the figure is

If $i_1=3 \sin \omega t$ and $i_2=4 \cos \omega t,$ then $i_3$ is

Each resistance shown in figure is $2 \mathrm{\Omega }$. The equivalent resistance between $A$ and $B$ is

Four resistors are connected as shown in the figure. It is found that the current flowing through the galvanometer $G$ is zero. The resistance of $R$ is

In the circuit shown in the figure, the current flowing in $2 \mathrm{\Omega }$ resistance is

The effective resistance between points $A$ and $\mathrm{B}$ is