A power system consists of $$300$$ buses out of which $$20$$ buses are generator buses, $$25$$ buses are the ones with reactive power support and $$15$$ buses are the ones with fixed shunt capacitors. All the other buses are load buses. It is proposed to perform a load flow analysis for the system using Newton-Raphson method. The size of the Newton-Raphson Jacobian matrix is

A list of relays and the power system components protected by the relays are given in List-$${\rm I}$$ and List-$${\rm II}$$ respectively. Choose the correct match from the four choices given below

List-$${\rm I}$$
$$A.$$ Distance relay
$$B.$$ Under frequency relay
$$C.$$ Differential relay
$$D.$$ Buchholz relay

List-$${\rm II}$$
$$1.$$ Transformers
$$2.$$ Turbines
$$3.$$ Busbars
$$4.$$ Shunt capacitors
$$5.$$ Alternators
$$6.$$ Transmission lines

The interrupting time of a circuit breaker is the period between the instant of

A three-phase alternator generating unbalanced voltages is connected to an unbalanced load through a 3-phase transmission line as shown in figure. The neutral of the alternator and the star point of the load are solidly grounded. The phase voltages of the alternator are
$${E_a} = 10\angle {0^ \circ }V,\,\,\,{E_b} = 10\angle - {90^ \circ }V,\,\,{E_c} = 10\angle {120^ \circ }\,\,V.\,\,\,\,$$ The positive sequence component of the load current is