Total instantaneous power supplied by a $$3$$-phase ac supply to a balanced $$R$$-$$L$$ load is

Bundled conductors are mainly used in high voltage overhead transmission lines to

A $$3$$-phase, $$11$$-$$kV$$ generator feeds power to a constant power unity power factor load of $$100$$ $$MW$$ through a $$3$$-phase transmission line. The line-to-line voltage at the terminals of the machine is maintained constant at $$11$$ $$kV$$. The per unit positive sequence impedance of the line based on $$100$$ $$MVA$$ and $$11$$ $$kV$$ is $$j$$ $$0.2$$. The line to line voltage at the load terminals is measured to be less than $$11$$ $$kV$$. The total reactive power to be injected at the terminals of the load to increase the line-to-line voltage at the load terminals to $$11$$ $$kV$$ is

A long wire composed of a smooth round conductor runs above and parallel to the ground (assumed to be a large conducting plane). A high voltage exists between the conductor and the ground. The maximum electric stress occurs at