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 $J$)

Three identical resistors $R_1 = R_2 = R_3 = R$ are connected as shown to a battery of constant e.m.f. $V$. The power dissipated is:

The total power dissipated in watts in the circuit shown is ............. $W$.

$A$ 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

$A$ ring is made of a wire having a resistance $R_0 = 12 \,\Omega$. Find the points $A$ and $B$,as shown in the figure,at which a current-carrying conductor should be connected so that the resistance $R$ of the sub-circuit between these points is equal to $\frac{8}{3} \,\Omega$.

The resistive network shown below is connected to a $D.C.$ source of $16 \, V$. The power consumed by the network is $4 \, W$. The value of $R$ is ............. $\Omega$.