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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.
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Surge Impedance: An important factor in the design of Transmission Lines.

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Characteristic Impedance or Surge Impedance is a term defined for a transmission line which tells us about the impedance that will be provided by the line to a surge flowing through it. Surge is a sudden high voltage spike which remains there for a short duration but can make an entire power system unstable. This happens either due to sudden switching or due to a lightning strike on the line.   For an ideal lossless transmission line, the surge impedance is given as the square root of line inductance to the shunt capacitance (capacitance between line and earth) i.e, sqrt(L/C). The ideal lossless line behaves as a pure inductor and hence its capacitance is zero so the surge impedance is sqrt(L/0) i.e, infinite. That's why the surge current can't flow through the line. On the other hand, the shunt capacitance is a pure capacitor and hence the impedance it provides to the surge current is sqrt(0/C) i.e, 0. So, the shunt capacitance provides a short circuit path to the surg...
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