The resistance of each wire between any two adjacent dots is $R$. Then the equivalent resistance between $A$ and $B$ as shown in the figure is:

Two bulbs,one of $50\, W$ and another of $25\, W$,are connected in series to the mains. The ratio of the currents through them is:

Two known resistances of $R \ \Omega$ and $2R \ \Omega$ and one unknown resistance $X \ \Omega$ are connected in a circuit as shown in the figure. If the equivalent resistance between points $A$ and $B$ in the circuit is $X \ \Omega$, then the value of $X$ is . . . . . . $\Omega$.

An electric kettle has two heating coils. When one coil is used,water in the kettle boils in $5$ minutes,while when the second coil is used,the same water boils in $10$ minutes. If the two coils,connected in parallel,are used simultaneously,the same water will boil in time:

The equivalent resistance between $A$ and $B$ for the mesh shown in the figure is ......... $\Omega$.

Two wires of the same material and equal length are joined in parallel combination. If one of them has half the thickness of the other and the thinner wire has a resistance of $8\, \Omega$,the resistance of the combination is equal to