In this circuit,when a certain current flows,the heat produced in the $5 \Omega$ resistor is $4.05 \ J$ in a time $t$. The heat produced in the $2 \Omega$ resistor in the same time interval is: (in $J$)

$A$ copper wire of resistance $R$ is cut into ten parts of equal length. Two pieces each are joined in series and then five such combinations are joined in parallel. The new combination will have a resistance

Three resistances of equal values $R$ are arranged in four different configurations as shown in the figure. The power dissipation in increasing order is:

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

You are given $n$ resistors each of resistance $r$. They are first connected to get the minimum possible resistance. In the second case,they are again connected differently to get the maximum possible resistance. Calculate the ratio between minimum and maximum values of resistance so obtained.

$A$ piece of wire is cut into four equal parts and the pieces are bundled together side by side to form a thicker wire. Compared with that of the original wire,the resistance of the bundle is ..........