The input voltage $v(t)$ and current $i(t)$ of a converter are given by, $v(t)=300 \sin (\omega t) \mathrm{V}$

$$ i(t)=10 \sin \left(\omega t-\frac{\pi}{6}\right)+2 \sin \left(3 \omega t+\frac{\pi}{6}\right)+\sin \left(5 \omega t+\frac{\pi}{2}\right) A $$

where, $\omega=2 \pi \times 50 \mathrm{rad} / \mathrm{s}$. The input power factor of the converter is closest to

The transformer connection given in the figure is part of a balanced 3-phase circuit where the phase sequence is "abc". The primary to secondary turns ratio is $2: 1$. If ( $I_a+I_b+I_c=0$ ), then the relationship between $l_A$ and $l_{\text {ad }}$ will be

Consider two coupled circuits having self inductances $L_1$ and $L_2$ that carry non-zero currents $I_1$ and $I_2$ respectively. The mutual inductance between the circuit is $M$ with unity coupling coefficient. The stored magnetic energy of the coupled circuit is minimum at which of the following value(s) of $I_1 / I_2$ ?

The switch ( S ) closes at $t=0 \mathrm{sec}$. The time, in sec the capacitor takes to charge to 50 V is __________ . (Round off to one decimal places)