A dc distribution system is shown in figure with load currents as marked. The two ends of the feeder are fed by voltage sources such that $${V_P} - {V_Q} = 3V.$$ the value of the voltage $${V_P}$$ for a minimum voltage of $$220$$ $$V$$ at any point along the feeder is

A surge of 20 kV magnitude travels along a lossless cable towards its junction with two identical lossless overhead transmission lines. The inductance and the capacitance of the cable are 0.4 mH and 0.5 $$\mu F$$ per km. The inductance and capacitance of the overhead transmission lines are 1.5 mH and 0.015 $$\mu F$$ per km. The magnitude of the voltage at the junction due to surge is

A balanced delta connected load of $$\left( {8 + j6} \right)\Omega $$ per phase is connected to a $$400$$ $$V$$, $$50$$ $$Hz$$, $$3-$$phase supply lines. If the input power factor is to be improved to $$0.9$$ by connecting a bank of star connected capacitors the required KVAR of the bank is

The conductors of a $$10$$ km long, single phase, two wire line are separated by a distance of $$1.5$$ m. The diameter of each conductor is $$1$$ cm. If the conductors are of copper, the inductance of the circuit is