The power dissipated in the circuit shown in the figure is $30 \, W$. The value of $R$ is ............. $\Omega$.

Two bulbs of $100\, W, 220\, V$ and $200\, W, 220\, V$ are connected in series to a $220\, V$ supply. What is the total power consumed in $W$?

The effective resistance between points $A$ and $B$ for the following network is (each branch has a resistance of $R$):

$A$ ring is made of a wire having a resistance $R_0 = 12 \,\Omega$. Find the points $A$ and $B$,as shown in the figure,at which a current-carrying conductor should be connected so that the resistance $R$ of the sub-circuit between these points is equal to $\frac{8}{3} \,\Omega$.

$A$ conductor of resistance $3 \Omega$ is stretched uniformly until its length is doubled. The wire is now bent in the form of an equilateral triangle. The effective resistance between the ends of any side of the triangle in ohms is

$A$ wire of resistance $R$ is bent into a circle of radius $r$. What is the equivalent resistance between points $X$ and $Y$?