As shown in the figure,the power dissipated in the $6\,\Omega$ resistor is $6\,W$. The power dissipated in the $4\,\Omega$ resistor will be: (in $,W$)

$A$ uniform metallic wire carries a current of $2\,A$ when a $3.4\,V$ battery is connected across it. The mass of the uniform metallic wire is $8.92 \times 10^{-3}\,kg$,its density is $8.92 \times 10^3\,kg/m^3$,and its resistivity is $1.7 \times 10^{-8}\,\Omega\cdot m$. The length of the wire is $l = \dots\dots\dots\dots\,m$.

In the diagram,the resistance between any two adjacent junctions is $R$. The equivalent resistance across terminals $A$ and $B$ is:

Two long coaxial and conducting cylinders of radius $a$ and $b$ are separated by a material of conductivity $\sigma$ and a constant potential difference $V$ is maintained between them by a battery. Then the current per unit length of the cylinder flowing from one cylinder to the other is -

Water boils in an electric kettle in $15\,\text{min}$ after switching on. If the length of the heating wire is decreased to $2/3$ of its initial value,then the same amount of water will boil with the same supply voltage in ............. $\text{min}$.

$A$ current of $6 \ A$ enters one corner $P$ of an equilateral triangle $PQR$ having three wires of resistance $2 \ \Omega$ each and leaves by the corner $R$ as shown in the figure. Then the currents $I_1$ and $I_2$ are respectively: