## The Mechanical Engineer’s Electrical Equation

I’ve been asked by mechanical engineering students which equations or concepts I use most often.  I’m sure they imagine I’ll give them a deflection equation or something from a mechanics text, but as much as I hate admitting this, the equation I use more than any other in my career as a mechanical engineer is straight out of Electrical Engineering 101, and that’s V=IR.

Keep in mind, I package power electronics, so while I occasionally reference plate deflection equations and sometimes pull out complex trigonometry and geometry, every system I’ve worked has required me to calculate voltage drop and current carrying capacity.

Let’s take bus bars for an example.  A bus bar is basically a lump of metal that carries a boat load of current from point A to point B.  The requirements are typically a minimum amount of current, a maximum allowed voltage drop, and a distance between points.  As with most hardware, bus bar design includes many nuances (contact pressure at the interfaces, for one), and the problem is further complicated when a weight limit enters the trade, but all of those nuances and factors can be worked back into our fundamental equation.

In simple form, you have to account for voltage drop through the bus bar body, as well as across the interface between the bus bar and terminal point, so we apply V=IR to both cases and we end up with:

Figure 1: Bus bar voltage drop calculations.

In the name of full disclosure, that contact resistance term is a bit of a cheat, and can be expanded by a page’s worth of additional equations, which will be the subject of a future post, but the derivations above should illustrate how versatile V=IR can be.

And it’s effectively the same for Printed Circuit Boards or wired harnesses. Any time you’re designing a component or structure through which power is transmitted, that’s the equation you need, and when you’re packaging power electronics, you design a lot of those components.

So even though V=IR is taught as an electrical engineering concept, its governing principles are almost exclusively mechanical in nature.  Resistance is determined by geometry and material properties.  Voltage drop is in turn determined by the resistance.  So it’s really a mechanical engineering equation.

In fact, now that I think about it, I’m positive I use it more often than my EE team members do…

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