Four wires $AB, BC, CD, DA$ of resistance $4\, \Omega$ each and a fifth wire $BD$ of resistance $8\, \Omega$ are joined to form a rectangle $ABCD$,where $BD$ is a diagonal. The effective resistance between the points $A$ and $B$ is:

Two electric bulbs ($60\,W$ and $100\,W$ respectively) are connected in series. The current passing through them is

The equivalent resistance between points $A$ and $B$ in the given network is ............ $\Omega$.

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

$A$ wire of resistance $R$ is cut into $8$ equal pieces. From these pieces,two equivalent resistances are made by connecting four of these pieces in parallel in each set. Then,these two sets are connected in series. The net effective resistance of the combination is

The equivalent resistance between ends $A$ and $B$ is