The voltage across the $10 \, \Omega$ resistor in the given circuit is $x$ volt. The value of $x$ to the nearest integer is..........

The power dissipated in the circuit shown in the figure is $30 \, W$. The value of $R$ is ............. $\Omega$.

Two resistance wires on joining in parallel the resultant resistance is $\frac{6}{5} \ \Omega$. One of the wires breaks,the effective resistance is $2 \ \Omega$. The resistance of the broken wire is ............ $\Omega$.

Two identical heater filaments are connected first in parallel and then in series. At the same applied voltage,the ratio of heat produced in the same time for parallel to series will be:

$A$ Copper $(Cu)$ rod of length $25 \, cm$ and cross-sectional area $3 \, mm^2$ is joined with a similar Aluminium $(Al)$ rod as shown in the figure. Find the resistance of the combination between the ends $A$ and $B$ (in $m\Omega$).
(Take Resistivity of Copper $= 1.7 \times 10^{-8} \, \Omega \cdot m$,Resistivity of Aluminium $= 2.6 \times 10^{-8} \, \Omega \cdot m$)

$A$ straight uniform wire of resistance $36 \Omega$ is bent in the form of a semi-circular loop. The effective resistance between the ends of the diameter of the semi-circular loop is