A water boiler at home is switched on to the $$A.C$$ mains supplying power at $$230$$ $$V/50$$ $$Hz.$$ The frequency of instantaneous power consumed by the boiler is

The moving coil in a dynamometer wattmeter is connected

In an oscilloscope the input to the horizontal plates is a $$100Hz$$ voltage signal. The lissajous patterns $$(A), (B)$$ and $$(C)$$ will be generated when different frequency voltage signals are applied to vertical plates. Match each lissajous pattern to the corresponding frequency by

In Figure. The characteristic that corresponds to the variation of synchronous reactance of synchronous motor with field current is