In a Wheatstone bridge,$P = 90\,\Omega$,$Q = 110\,\Omega$,$R = 40\,\Omega$,and $S = 60\,\Omega$. $A$ cell of $4\,V$ emf is connected across the input terminals. The potential difference between the diagonal points $B$ and $C$ (where the galvanometer is connected) is ............. $V$.

Kirchhoff's first law $(\sum i = 0)$ and second law $(\sum iR = \sum E)$,where the symbols have their usual meanings,are respectively based on:

In the circuit shown in the figure,$P \neq R$. The reading of the galvanometer remains the same with switch $S$ open or closed. Then

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

The figure below shows currents in a part of an electric circuit. The current $i$ is ............. $A$.

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 $2R_1=R_2=R_3$