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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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If two coils are wound on a wooden core insulated from each other, will there be mutual inductance between them?

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Yes for small power like RF application, wooden core is used. Wood has permeability almost equal to that of air. Most of the RF applications require air core winding which removes the complexity of non-linear behavior of a magnetic core having low reluctance. That's why such a core can't be pushed into saturation and the reluctance strictly depends on mean core length (lg) and area of cross section (Ag) given by the relation

Reluctance, R=lg/µAg

Where µ is the permeability. Permeability simply means the ease with which magnetic flux can pass through a material. As seen, Reluctance increases with decreasing µ and vice versa, hence the reluctance called as magnetic resistance. For higher power application it is not suitable but windings which require air core can use woods (and are used to provide strength and rigidness to the windings). Here µ can be called permeability of air which is 4π×10^(-7).

A good material used for core in power applications is Silicon Steels or even better CRGO steel. CRGO steels have low reluctance in the path of flow of flux and comparatively high in the other directions. CRGO steels are used as cores to power transformers.

P.S. You can compare magnetic flux to electric current and reluctance to impedance. The current always follows the path of least impedance. Similarly the flux choses path if minimum reluctance (the voltage source can be compared to MMF if you want to know which is equal to product of Amperes and turns). So, we can increase the mmf by increasing number of turns which would give us required flux as Reluctance is a constant quantity. Moreover, the required inductance also increases as the square of number of turns as it is given by

L=µ(N^2)A/l

A being area of cross section and l being length of the coil (length of coil means length of the winding not the conductor).

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