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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.
 
Transmission line surges

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 surge. In this way, the line is protected from the surge.

In reality, there are some losses that happen in the line due to line resistance and shunt conductance. However, the line is so made that the resistance and shunt conductance remains negligible. Also, additional shunt capacitors are added to the line to provide a short circuit path to the surge current and hence limit it to short distance on the line. Longer transmission lines operate at high voltages and have a higher value of inductance thus higher surge impedance. So, it can naturally protect itself against surges and maintain line stability.

However, higher surge impedance limits the loading capability of the line and hence very high value is undesirable and thus a trade-off between natural protection and power transfer capability is important in the design and installation of transmission lines.

Let me know your questions, feedback and suggestions, if any, in the comment section below



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