In the given circuit, the values of currents $I_1$, $I_2$ and $I_3$ respectively are:

In the following network,the current through the galvanometer will:

Two ideal batteries of emf $V_1$ and $V_2$ and three resistances $R_1, R_2$ and $R_3$ are connected as shown in the figure. The current in resistance $R_2$ would be zero if:
$(A)$ $V_1=V_2$ and $R_1=R_2=R_3$
$(B)$ $V_1=V_2$ and $R_1=2R_2=R_3$
$(C)$ $V_1=2V_2$ and $2R_1=2R_2=R_3$
$(D)$ $2V_1=V_2$ and $2R_1=R_2=R_3$

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 $\Omega$.

In the given circuit diagram,the currents $I_1 = -0.3\,A$,$I_4 = 0.8\,A$ and $I_5 = 0.4\,A$ are flowing as shown. The currents $I_2, I_3$ and $I_6$ respectively are

Five equal resistances are connected in a network as shown in the figure. The net resistance between the points $A$ and $B$ is