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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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What's inside a Fluorescent Lamp Starter? Let's find out.

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So, I was repairing this old LED light which had a defect in its filter capacitor. In the meantime, I wanted to find out what happens if I connect a fluorescent lamp starter with this LED circuit in series just as it is in case of a Fluorescent Lamp? So, I broke the plastic cover and took out this actual starter inside which has a capacitor* connected in parallel to. Here's what I found. 
 


 *Note: The capacitor that you see in parallel to the starter is there to force high voltage across the bimetallic strip to make the entire process faster. In a fluorescent tube, fast starting is very much important to create a huge voltage across the lamp filaments and help it getting ignited.

Video on working of a Fluorescent Lamp Tube: https://youtu.be/whMsyZmwEGU


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