In the following circuit,the battery has an emf of $2 \ V$ and an internal resistance of $\frac{2}{3} \ \Omega$. The power consumption in the entire circuit is $..... \ W$.

Under what conditions can the current passing through a 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.

The currents $i_1$ and $i_2$ through the resistors $R_1 (= 10\,\Omega)$ and $R_2 (= 30\,\Omega)$ in the circuit diagram with $E_1 = 3\,V, E_2 = 3\,V$ and $E_3 = 2\,V$ are respectively:

Two bulbs rated $25 \ W - 220 \ V$ and $100 \ W - 220 \ V$ are connected in series to a $440 \ V$ supply. Which of the following happens?

Two infinite circuits (shown below) are called 'Circuit $A$' and 'Circuit $B$'. The equivalent resistance of 'Circuit $A$' is $x$ and that of 'Circuit $B$' is $y$ between terminals $1$ and $2$.

The circuit diagram shown consists of an infinite number of elements (each element has two resistors $R_1$ and $R_2$). The resistance of the resistors in each subsequent element differs by a factor of $K = 1/2$ from the resistance of the resistors in the previous elements. The equivalent resistance between $A$ and $B$ shown in the figure is: