Three resistances of $1\, \Omega$ each are connected in parallel. Such a connection is then connected in series with a $\frac{2}{3}\, \Omega$ resistor. The resultant resistance will be ........... $\Omega$.

The equivalent resistance between the points $P$ and $Q$ in the network given here is equal to ................ $\Omega$ (given $r = \frac{3}{2} \Omega$).

$A$ ring is made of a wire having a resistance $R_0 = 12\,\Omega$. Find the ratio of the lengths $\frac{l_1}{l_2}$ of the two arcs between points $A$ and $B$ as shown in the figure,such that the equivalent resistance $R$ of the sub-circuit between these points is equal to $\frac{8}{3}\,\Omega$.

The lowest resistance which can be obtained by connecting $10$ resistors each of $1/10$ $\Omega$ is

Consider the following two circuits:
$A$: $20$ bulbs are connected in series to a power supply line.
$B$: $20$ bulbs identical to $A$ are connected in a parallel circuit to an identical power supply line.
Identify which of the following is not true.

The equivalent resistance of three unequal resistors connected in parallel is $1 \ \Omega$. If the ratio of two of them is $1:2$ and all resistance values are integers,what is the value of the largest resistor in ohms?