Resistors of $4\, R, 16\, R, 64\, R, \dots \infty$ are connected in series. Find their equivalent resistance.

$A$ 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

When two resistors of $R \ \Omega$ value are connected in parallel,what is the equivalent resistance?

An electric kettle has two heating coils. When one of the coils is connected to an a.c. source,the water in the kettle boils in $10$ minutes. When the other coil is used,the water boils in $40$ minutes. If both the coils are connected in parallel,the time taken by the same quantity of water to boil will be ...... $min$.

$A$ wire of resistance $R$ is bent into an equilateral triangle and an identical wire is bent into a square. The ratio of the equivalent resistance between the two end points of an edge of the triangle to that of the square is

As shown in the figure,$13$ resistors each of resistance $R$ are connected. The effective resistance between points $A$ and $B$ is: