Find the equivalent resistance between point $A$ and $B$ in the following circuit. (The resistance of each resistor is $R$)

The equivalent resistance between the points $A$ and $D$ is ................ $\Omega$.

Five identical resistors are initially arranged as shown in the figure by solid lines. If two identical resistors are added as shown by the dashed lines,the change in the equivalent resistance between the initial and final configurations is ....... $\Omega$.

The potential difference between the points $P$ and $Q$ in the circuit shown is: (in $\text{ V}$)

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

Different combinations of $3$ resistors of equal resistance $R$ are shown in the figures. The increasing order for power dissipation is: