In the given circuit,$a$ is an arbitrary constant. The value of $m$ for which the equivalent circuit resistance is minimum is given by $\sqrt{\frac{x}{2}}$. The value of $x$ is:

$A$ heater coil connected to a supply of $220 \ V$ is dissipating some power $P_1$. The coil is cut into half and the two halves are connected in parallel. The heater now dissipates a power $P_2$. The ratio of power $P_1 : P_2$ is

What is the equivalent resistance between $A$ and $B$?

$A$ 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 of the legs is close to ................ $\Omega$.

Four wires of equal length and of resistances $10 \ \Omega$ each are connected in the form of a square. The equivalent resistance between two opposite corners of the square is ............. $\Omega$. (in $\Omega$)

$A$ 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