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?

In the circuit shown, the phase currents are

$$ \begin{aligned} & I_A=572.812+j 50.115 \mathrm{~A} \\ & I_B=-254.525-j 459.175 \mathrm{~A} \\ & I_C=-207.083+j 444.091 \mathrm{~A} \end{aligned} $$

Given that the CTs are ideal with no saturation, and the turns ratio of the Main CT is $300: 5$ and that of the Auxiliary Transformer $(Y n \Delta)$ is $2: 1$ on every phase, the value of $I_{A R}$, rounded off to three decimal places, is