A particle of mass $$10 \mathrm{~g}$$ moves in a straight line with retardation $$2 x$$, where $$x$$ is the displacement in SI units. Its loss of kinetic energy for above displacement is $$\left(\frac{10}{x}\right)^{-n}$$ J. The value of $$\mathrm{n}$$ will be __________

The length of a metallic wire is increased by $$20 \%$$ and its area of cross section is reduced by $$4 \%$$. The percentage change in resistance of the metallic wire is __________.

A parallel plate capacitor with plate area $$\mathrm{A}$$ and plate separation $$\mathrm{d}$$ is filled with a dielectric material of dielectric constant $$K=4$$. The thickness of the dielectric material is $$x$$, where $$x < d$$.

Let $$\mathrm{C}_{1}$$ and $$\mathrm{C}_{2}$$ be the capacitance of the system for $$\chi=\frac{1}{3} d$$ and $$\mathcal{X}=\frac{2 d}{3}$$, respectively. If $$\mathrm{C}_{1}=2 \mu \mathrm{F}$$ the value of $$\mathrm{C}_{2}$$ is __________ $$\mu \mathrm{F}$$

An ideal transformer with purely resistive load operates at $$12 ~\mathrm{kV}$$ on the primary side. It supplies electrical energy to a number of nearby houses at $$120 \mathrm{~V}$$. The average rate of energy consumption in the houses served by the transformer is 60 $$\mathrm{kW}$$. The value of resistive load $$(\mathrm{Rs})$$ required in the secondary circuit will be ___________ $$\mathrm{m} \Omega$$.