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 $J$)

$A$ wire of resistance $R$ is cut into $n$ equal parts. These parts are then connected in parallel. The equivalent resistance of the combination will be

Six wires, each of resistance $r$, are connected so as to form a tetrahedron. The equivalent resistance of the combination when current enters through one corner and leaves through some other corner is

$A$ uniform conductor of resistance $R$ is cut into $20$ equal pieces. Half of them are joined in series and the remaining half of them are connected in parallel. If the two combinations are joined in series,the effective resistance of all the pieces is

In the figure given,the electric current flowing through the $5\, k\Omega$ resistor is $'x' \, mA.$
The value of $x$ to the nearest integer is .........

If the ratio of the equivalent resistance of two resistors $R_1$ and $R_2$ in series to that in parallel is $n$,then: