In an a.c. circuit with pure capacitance 'C' and a.c. source $E = E_0\sin\omega t$, the equation of instantaneous current is given by

In a series LCR circuit alternating e.m.f. and current are given by the equations $V = V_0\sin(\omega t)$ and $I = I_0\sin\left(\omega t + \dfrac{\pi}{3}\right)$ respectively. The average power dissipated in the circuit over one cycle of a.c. is $(\cos 60^\circ = 0.5)$

A ray of light incident on one face of an equilateral glass prism having refractive index $\sqrt{2}$, produces the emergent ray which just grazes along the adjacent face. The value of angle of incidence is $(\sin 90^\circ = 1)$
$\left(\sin 30^\circ = \dfrac{1}{2}\right)\left(\sin 45^\circ = \dfrac{1}{\sqrt{2}}\right)$

An unpolarised light of intensity $64 \text{ Wm}^{-2}$ passes through three polarizers successively such that the transmission axis of last polarizer is crossed with the first. The intensity of the emerging light is $6 \text{ Wm}^{-2}$. The angle between the transmission axis of the first two polarizers is