Two resistors of resistance $100\,\Omega$ and $200\,\Omega$ are connected in parallel in an electrical circuit. The ratio of the thermal energy developed in $100\,\Omega$ to that in $200\,\Omega$ in a given time is:

$A$ wire has a resistance of $6 \,\Omega$. It is cut into two equal parts and both parts are connected in parallel. The new resistance is ................ $\Omega$.

The effective resistance of a parallel connection that consists of four wires of equal length,equal area of cross-section,and same material is $0.25\, \Omega$. What will be the effective resistance if they are connected in series? (In $\Omega$)

Resistors $R, 2R, 4R, 8R, ..... \infty$ are connected in parallel. What is their equivalent resistance?

For the shown circuit,find the effective resistance between the points $A$ and $B$.

$A$ uniform wire of resistance $9 \, \Omega$ is bent in the form of a circle. The effective resistance across the points $A$ and $B$ is ............... $\Omega$. The angle subtended by the arc $AB$ at the center is $120^{\circ}$.