$A$ battery of $e.m.f.$ $10 \, V$ and internal resistance $3 \, \Omega$ is connected to a resistor $R$ as shown in the figure. If the current in the circuit is $0.5 \, A$,then the resistance of the resistor $R$ will be ............. $\Omega$.

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 e.m.f. of a cell is $E \text{ volts}$ and its internal resistance is $r \text{ ohm}$. The resistance in the external circuit is also $r \text{ ohm}$. The potential difference across the cell will be

The figure shows a network of resistances and cells in which the point $A$ is earthed. The point which has the least potential is

Identical resistors of resistance $R$ are connected as shown in the figure. Find the equivalent resistance between $x$ and $y$.

One end each of a resistance $r$,a capacitor $C$,and a resistance $2r$ are connected together. The other ends are respectively connected to the positive terminals of batteries $P$,$Q$,and $R$ having emfs $E$,$E$,and $2E$. The negative terminals of the batteries are then connected together. In this circuit,with steady current,the potential drop across the capacitor is: