Two identical heaters rated $220\,V, 1000\,W$ are connected in series across a $220\,V$ supply. If the resistance does not change with temperature,the total power consumed by the combination is ............. $W$.

Six resistances each of value $r = 6\,\Omega$ are connected between points $A, B$ and $C$ as shown in the figure. If $R_1, R_2$ and $R_3$ are the net resistance between $A$ and $B$,between $B$ and $C$,and between $A$ and $C$ respectively,then $R_1 : R_2 : R_3$ will be equal to:

$A$ conductor of resistance $3 \Omega$ is stretched uniformly until its length is doubled. The wire is now bent in the form of an equilateral triangle. The effective resistance between the ends of any side of the triangle in ohms is

Three resistances $2 \Omega, 3 \Omega$ and $4 \Omega$ are connected in parallel. The ratio of currents passing through them when a potential difference is applied across its ends will be

The effective resistance across $AB$ in the network shown is .......... $\Omega$.

Explain the series connection of resistors. Derive the equation for the equivalent resistance $(R_S)$.