Two $10\,\Omega$ resistors are first connected in series and then in parallel. What is the ratio of the equivalent resistance in both cases?

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

In the given star circuit,find the equivalent resistance between $A$ and $H$. (in $r$)

$A$ letter $A$ is constructed of a uniform wire with resistance $1.0\,\Omega/cm$. The sides of the letter are $20\,cm$ and the cross-piece in the middle is $10\,cm$ long. The apex angle is $60^\circ$. The resistance between the ends $A$ and $D$ is ............. $\Omega$.

Consider the ladder network shown in the figure. What should be the value of resistance $R$ so that the effective resistance between $A$ and $B$ becomes independent of the number of elements in the combination? ............. $\Omega$

$A$ current of $3 \, A$ flows through the $2 \, \Omega$ resistor shown in the circuit. The power dissipated in the $5 \, \Omega$ resistor is ................. $W$.