Three resistances $2 \Omega, 3 \Omega$ and $4 \Omega$ are connected in parallel. The ratio of currents passing through them when a potential difference is applied across its ends will be

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

$A$ heating coil can heat the water of a vessel from $20\,^oC$ to $60\,^oC$ in $30$ minutes. Two such heating coils are put in series and then used to heat the same amount of water through the same temperature range. The time taken now will be ............ $min$ (neglecting thermal capacity of the coils).

Find the equivalent resistance between the two ends of the following circuit.

There are $8$ equal resistances $R$. Two are connected in parallel,and such four groups are connected in series. The total resistance of the system will be:

$A$ wire of resistance $12 \, \Omega$ is bent to form an equilateral triangle. What is the equivalent resistance between any two corners of the triangle?