Following two circuits $A$ and $B$ are designed to control brightness of an $18 \mathrm{W}$ bulb. Each circuit consists of a light bulb rated at $18 \mathrm{W}$ and $12 \mathrm{V}$, a variable resistor, an ideal $12 \mathrm{V}$ battery and a $2 \mathrm{A}$ fuse with negligible resistance.

 

In the given circuit, an ideal voltmeter connected across the $10 \mathrm{\Omega }$ resistance reads $2\mathrm{ }\mathrm{V}$ . The internal resistance $r$, of each cell is:

Six similar bulbs are connected as shown in the figure with a DC source of emf $E$, and zero internal resistance.
The ratio of power consumption by the bulbs when $\left(\mathrm{i}\right)$ all are glowing and $\left(\mathrm{ii}\right)$ in the situation when two from section $A$ and one from section $B$ are glowing will be, 

The diagram above shows a circuit with the key k open.

 Calculate the resistance of the circuit when the key k is closed.

 Calculate the current drawn from the cell when the key k is closed.

The variation of terminal potential difference $\left(V\right)$ with current flowing through as cell is as shown

The $\mathrm{emf}$ and internal resistance of the cell are

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