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

A 3-phase transmission line supplies $$\Delta - $$ connected load Z. The conductor $$'c'$$ of the line develops an open circuit fault as shown in figure. The currents in the lines are as shown on the diagram. The +ve sequence current component in line 'a' will be

A new generator having $${E_g} = 1.4\,\angle {30^ \circ }\,$$ pu [ equivalent to ($$1.212 +j$$ $$0.70$$)pu ] and synchronous reactance $$'{X_s}'$$ of $$1.0$$ pu on the system base, is to be connected to a bus having voltage $${V_t}$$ in the existing power system. This existing power system can be represented by Thevenin's voltage $${E_{th}} = 0.9\angle {0^ \circ }\,\,$$ pu in series with Tjhevenin's impedance $${Z_{th}} = 0.25\angle {90^ \circ }\,\,$$ pu. The magnitude of the voltage $${V_t},$$ of the system in pu will be

For harnessing low variable water heads, the suitable hydraulic turbine with high percentage of reaction and runner adjustable vanes is