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the inducedd e.m.f and the change in magnetic flux have opposite direction

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Q: Why a negative sign appears in the equation of faradays law of electromagnetic induction?
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When slip motor is negative what conduction obtained?

Your question can not be answered as it is. Reword the question - is it about induction motors or synchronous motors, for example?


What power generated in wind power generation AC or DC?

Any generator that rotates will naturally generate AC power into the stationary winding. Wind generators are (all I believe, but could be wrong) induction machines, meaning an AC source is applied to the field and an AC output is generated in the stator. Just like an induction motor, the machine operates with some slip (the rotor speed + the field power frequency = the stator power frequency). If the machine is turning above synchronous speed (so the slip is negative in my equation), the machine will be generating power instead of using it.


Without solving the equation determine the nature of the roots of 2x 2 plus 3x plus 9 0?

With a negative discriminant, the two solutions are imaginary.


When the induction motor working as induction generator?

An induction motor connected to an existing ac supply normally runs at less than the synchronous speed by an amount described as the 'slip' which is proportional to the torque demanded at the shaft. If the same motor is instead coupled to an engine and driven at a speed higher than the synchronous speed, with negative slip, power then travels back into the ac supply and the motor has become a generator. The amount of power produced depends on the speed. However a normal induction motor will not behave as a stand-alone ac generator. For ac power generation synchronous generators are invariably used because it is necessary to set and maintain the frequency of the supply accurately.


How does single phase induction motor varies from 3 phase induction motor?

All induction motors require a rotating magnetic field in order to drive their rotors. Unlike a three-phase motor, a single-phase induction motor does not have a naturally-rotating magnetic field set up in the air gap between the stator and rotor and, so, this rotating magnetic field must be artificially created by stator windings that are roughly 90 degrees out of phase with each other. In most cases, this is done by inserting a capacitor in what is termed its 'auxiliary winding'.