In an a.c. circuit the instantaneous current and emf are represented as $$\mathrm{I}=\mathrm{I}_0, \sin [\omega \mathrm{t}-\pi / 6]$$ and $$\mathrm{E}=\mathrm{E}_0 \sin [\omega \mathrm{t}+\pi / 3]$$ respectively. The voltage leads the current by

In a biprism experiment, monochromatic light of wavelength '$$\lambda$$' is used. The distance between two coherent sources '$$\mathrm{d}$$' is kept constant. If the distance between slit and eyepiece '$$\mathrm{D}$$' is varied as $$D_1, D_2, D_3 \& D_4$$ and corresponding measured fringe widths are $$Z_1, Z_2, Z_3$$ and $$Z_4$$ then

Three charges each of value $$+q$$ are placed at the corners of an isosceles triangle $$\mathrm{ABC}$$ of sides $$\mathrm{AB}$$ and $$\mathrm{AC}$$ each equal to $$2 \mathrm{a}$$. The mid points of $$A B$$ and $$A C$$ are $$D$$ and $$E$$ respectively. The work done in taking a charge $$Q$$ from $$D$$ to $$E$$ is ( $$\varepsilon_0=$$ permittivity of free space)

Light of frequency 1.5 times the threshold frequency is incident on photosensitive material. If the frequency is halved and intensity is doubled, the photocurrent becomes