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When to use I²R, V²/R or VI while calculating Electric Power?

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I came across a question that was asked to me quite a couple of time: When to use I²R, V²/R or VI while calculating power? At first, the question looks simple and as if it needs no formal explanation but that's not the case. Use of any of them will give the correct result provided that you apply it correctly. Correct application is possible only when you understand the type of circuit you are dealing with. Another important point is to use the one which is going to take less time and help you calculate easily. All of the three equations tell the same thing but their usage is subject to the type of problem you're trying to solve. Let us understand when, how an what to use while calculating power in an electrical circuit.

Effect of external rotor resistance on torque of an induction Motor.

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What causes change in rotor resistance externally in a three phase slip-ring induction motor to change its Torque? Slip-Ring Induction Motor (Credit: http://yourelectricalguide.com) While studying about induction motor types you must have come across this machine whereit has three conductors for rotor connected externally to a rheostat. But how exactly they help? Why do we need those rotor external resistance? Let's find out. The one line answer to this question most of the time people suggest is, "To increase the Motor Torque". Well I willn't say it's incorrect but it's vague or incomplete.  Torque in an induction motor depends on two things, air gap flux and rotor magnetic flux generated due to induced emf . When rotor cuts air gap flux, a current flows through rotor conductors. As a result, the rotor generates its own flux and hence under the effect of this stator and rotor flux, there is a resultant flux which us responsible for torque.

INDUCTION MOTOR - Working Principle & Analysis | EXPLAINED SIMPLY

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