Under what condition can the current passing through the resistance $R$ be increased by short-circuiting the battery of emf $E_2$? The internal resistances of the two batteries are $r_1$ and $r_2$ respectively.

Two cities are $150\, km$ apart. Electric power is sent from one city to another city through copper wires. The fall of potential per $km$ is $8\, V$ and the average resistance per $km$ is $0.5\, \Omega$. The power loss in the wire is

The battery in the diagram is to be charged by the generator $G$. The generator has a terminal voltage of $120 \ V$ when the charging current is $10 \ A$. The battery has an $emf$ of $100 \ V$ and an internal resistance of $1 \ \Omega$. In order to charge the battery at $10 \ A$ charging current,the resistance $R$ should be set at ................ $\Omega$.

In steady state, the potential difference across the capacitor is $10\, V$. Each resistance is of $3\, \Omega$. The cell is ideal. The $emf$ of the cell is ............. $V$.

In the given circuit,the current through $2 \ \Omega$ resistor is

Find the net emf of the three batteries shown in the figure. (in $, V$)