In a Wheatstone bridge,all the four arms have equal resistance $R$. If the resistance of the galvanometer arm is also $R$,the equivalent resistance of the combination as seen by the battery is

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 $2R_1=R_2=R_3$

In the given figure: $V_1=V, V_2=\alpha V, R_1=\beta R, R_2=\gamma R$,where $\alpha, \beta$,and $\gamma$ are positive real numbers. The value of current $I$ is

In the circuit shown in the figure,all the resistances are identical and each has the value $r \ \Omega$. The equivalent resistance of the combination between the points $A$ and $B$ will remain unchanged even when the following pairs of points marked in the figure are connected through a resistance $R$.

See the electrical circuit shown in the adjoining figure. Which of the following equations is a correct equation for it?

Five current-carrying conductors meet at a point $P$. Based on the provided image,what is the magnitude and direction of the current in the fifth conductor connected to point $Q$?