$A$ wire of resistance $100 \Omega$ is stretched so that its length increases by $20 \%$. The stretched wire is then bent in the form of a rectangle whose length and breadth are in the ratio $3: 2$. The effective resistance between the ends of any diagonal of the rectangle is (in $\Omega$)

The equivalent resistance between the terminals $A$ and $B$ is ............. $\Omega$.

Resistors $R, 2R, 4R, 8R, ..... \infty$ are connected in parallel. What is their equivalent resistance?

In the following star circuit diagram,the equivalent resistance between the points $A$ and $H$ will be ..............$r$.

In an aluminium $(Al)$ bar of square cross-section,a square hole is drilled and is filled with iron $(Fe)$ as shown in the figure. The electrical resistivities of $Al$ and $Fe$ are $2.7 \times 10^{-8} \ \Omega m$ and $1.0 \times 10^{-7} \ \Omega m$,respectively. The electrical resistance between the two faces $P$ and $Q$ of the composite bar is

$3$ identical bulbs are connected in series and these together dissipate a power $P$. If now the bulbs are connected in parallel,then the power dissipated will be