Alternating current of peak value $\left(\dfrac{2}{\pi}\right)$ A flows through the primary coil of a transformer. The coefficient of mutual inductance between primary and secondary coils is 1H. The peak value of induced e.m.f. in the secondary coil is
(Frequency of a.c. = 50 Hz)

Series LCR circuit containing an a.c. source of 100V has a inductor and a capacitor of reactance $24\ \Omega$ and $16\ \Omega$ respectively. If a resistance of $6\ \Omega$ is connected in series, then the potential difference across the series combination of inductor and capacitor only is

An inductor of inductance $2\ \mu\text{H}$ is connected in series with a resistance, a variable capacitor and an a.c. source of 10 kHz. The value of capacitance for which maximum current is drawn in to the circuit is $\dfrac{1}{x}\ \text{F}$, where the value of x is (Take $\pi^2 = 10$)

A ray of light passes from the vacuum into a medium of refractive index 'n'. If the angle of incidence is twice the angle of refraction, then the angle of incidence in terms of refractive index is