# Computing stuff tied to the physical world

## Energy, power, current, charge

In Hardware on May 14, 2013 at 00:01

The International System of Units, or SI from the French Système International is a wonderfully clever refinement of the original metric system.

Took me a while to get all this clear, but it really helps to understand electrical “units”:

• power says something about intensity: volts times amperes, the unit is watt
• energy says something about effort: power times duration, the unit is watt-second
• current says something about rate: charge per time unit, the unit is ampere
• charge says something about pressure: more charge raises volts, the unit is coulomb

Of course, some units get expressed differently – that’s just to scale things for practical use:

• a kilowatt (kW) is 1000 watts
• a watt-hour (Wh) is 3600 watt-seconds
• a kilowatt-hour (kWh) is 1000 watt-hour
• a milli-ampere (mA) is 1/1000 of an ampere
• a micro-coulomb (µC) is 1/1000000 of a coulomb

But there are several more useful equivalences:

• When a 1.5 V battery is specified as 2000 mAh (i.e. 2 Ah), then it can deliver 1.5 x 2 = 3 Wh of energy – why? because you can multiply and divide units just like you can with their quantities, so V x Ah = V x A x h = W x h = Wh
• Another unit of energy is the “joule” – which is just another name for watt-second. Or to put it differently: a watt is one joule per second, which shows that a watt is a rate.
• A joule is also tied to mechanical energy: one joule is one newton-meter, where the “newton” is the unit of force. A newton is what it takes to accelerate 1 kg of mass by 1 m/s2 (i.e. increase the velocity by 1 m/s in one second – are you still with me?).
• So the watt also represents a mechanical intensity (i.e. strength). Just like one horsepower, which is defined as 746 W, presumably the strength of a single horse…
• Got a car with a 100 Hp engine? It can generate 74.6 kW of power, i.e. accelerate a 1000 kg weight by 74.6 m/s2, which is ≈ 20 km/h speed increase every second, or in more popular terms: 0..100 km/h in 5 seconds (assuming no losses). But I digress…

The point is that all those SI units really make life easy. And they’re 100% logical…

1. The equivalence with the mechanical domain you mention is stunning indeed. It turns out that voltage is completely equivalent with force, and current with velocity. Try it: 1 V * 1 A = 1 W; 1 N * 1 m/s = 1 Nm/s = 1 J/s = 1 W.

What’s more: a mechanical spring is completely equivalent with a capacitor—the spring integrates the velocity you put into it, which gives you the total spring depression, and everyone knows F = (-)K * x. The capacitor integrates the current you put into it (giving total stored charge, Q), and V = 1/C * Q. Put it the other way around (differentiating left and right) and you arrive at the expression we all know: dV/dt = 1/C * dQ/dt = 1/C * i; or: i=C dv/dt.

The same way you can show that a mass is equivalent to a coil, and a friction to a resistor; and there you go: you can calculate/simulate the dynamics of a mechanical system the same way you would an electrical circuit.

The same equivalence also holds for hydraulics, by the way, and is much easier to see: current is volumetric flow, voltage is pressure; capacitors are water basins and coils (inductances) are long pipes with water flowing in them. You can hear the latter in old homes with copper piping: suddenly close a tap and you’ll hear a “bang” in the pipes of the water suddenly stopping. Try suddenly switching off a coil that carries current and you’ll see the electrical equivalent of this bang: a spark across the contacts!