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 ............. $\Omega$.

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

$6 \Omega$ and $12 \Omega$ resistors are connected in parallel. This combination is connected in series with a $10 \text{ V}$ battery and a $6 \Omega$ resistor. What is the potential difference between the terminals of the $12 \Omega$ resistor (in $\text{ V}$)?

Two resistors of resistance $100\,\Omega$ and $200\,\Omega$ are connected in parallel in an electrical circuit. The ratio of the thermal energy developed in $100\,\Omega$ to that in $200\,\Omega$ in a given time is:

The effective resistance between points $A$ and $B$ for the following network is (each branch has a resistance of $R$):

Four wires of equal length and of resistances $10 \ \Omega$ each are connected in the form of a square. The equivalent resistance between two opposite corners of the square is ............. $\Omega$. (in $\Omega$)