Consider the boost converter circuit shown. Assume that the semiconductor devices are ideal. In steady state, the inductor current rises linearly from 0 A to 6 A in the first $10 \mu \mathrm{~s}$ and then falls linearly from 6 A to 0 A in the next $10 \mu \mathrm{~s}$ of every switching cycle as shown. The load resistance R is $10 \Omega$ and the capacitance C is $50010 \mu \mathrm{~F}$.

Neglect the ripple in the output voltage. What is the input voltage $V_{d c}$ ?

Consider the circuit shown. Assume that the diode (D) is ideal.

Given $v_s=100 \sin (2 \pi 50 t) V_{d c}=50 \mathrm{~V}$, and $R=10 \Omega$, the average value of the current through the diode is $\_\_\_\_$ A. (Round off to two decimal places)

Consider a power system with $N$ buses, of which $P$ are generator buses and the remaining $Q$ are load buses (where there is no generation).

Assume that there are no reactive power-limit violations at the generator buses. What is the size of the Jacobian matrix in the Newton-Raphson load flow method?

The initial three-phase voltage phasors ( $\vec{V}_A, \vec{V}_B$, and $\vec{V}_C$ ) at a bus of a power network are as shown in Case-1. Due to a disturbance, the bus voltage phasors changed in phase by a small angle $\Delta \theta$, and the magnitudes remained the same as depicted in Case- 2 .

Which one of the following statements is correct about the zero sequence components?