It is desired to measure parameters of $$230$$ $$V/115$$ $$V,$$ $$2$$ $$kVA$$, single-phase transformers. The following watt-meters are available in a laboratory:
$${W_1}:250\,\,V,\,\,\,10\,\,A,\,\,\,\,\,\,$$ Low Power Factor
$${W_2}:250\,\,V,\,\,\,5\,\,A,\,\,\,\,\,\,$$ Low Power Factor
$${W_3}:150\,\,V,\,\,\,10\,\,A,\,\,\,\,\,\,$$ High Power Factor
$${W_4}:150\,\,V,\,\,\,5\,\,A,\,\,\,\,\,\,$$ High Power Factor

The watt-meters used in open circuit test and short circuit test of the transformer will respectively be

The core of two-winding transformer is subjected to a magnetic flux variation as indicated in the figure.

The induced $$emf$$ $$\left( {{e_{rs}}} \right)$$ in the secondary winding as a function of time will be of the form

A capacitor consists of two metal plates each $$500 \times 500\,\,m{m^2}$$ and spaced $$6$$ $$mm$$ apart. The space between the metal plates is filled with a glass plate of $$4$$ $$mm$$ thickness and a layer of paper of $$2$$ $$mm$$ thickness. The relative permittivity of the glass and paper are $$8$$ and $$2$$ respectively. Neglecting the fringing effect, the capacitance will be (Given that $${\varepsilon _0} = 8.85 \times {10^{ - 12}}\,F/m$$ )

Two point charges $${Q_1} = 10\,\,\mu C$$ and $${Q_2} = 20\,\,\mu C$$ are placed at coordinates $$(1,1,0)$$ and $$\left( { - 1, - 1,0} \right)$$ respectively. The total electric flux passing through a plane $$z=20$$ will be