Kirchhoff's first law,$i.e.$,$\Sigma i = 0$ at a junction,is based on the law of conservation of:

Kirchhoff's first law $(\Sigma i = 0)$ and second law $(\Sigma iR = \Sigma E)$ are based on which of the following respectively? (Where the symbols have their usual meanings.)

In the given electrical circuit,which one of the following equations is correct?

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 $2R_1=R_2=R_3$

For the network shown in the figure,the value of the current $i$ is:

The figure shows a network of four resistances and three batteries. Choose the correct alternative.