The Other Side of Network of Dr. Charles Kim

I welcome your questions and comments. -Charles Kim. Email to me at ckimson@gmail.com

The Laws of Circuit - you can learn and practice by just reading

Five Tau (t) Rule

Five Second Rule

If you are old enough and have a kid or two, you say this rule quite often or, at least, try. If you are still young (and restless), you still remember this rule often heard too late to do anything at all: you already swallowed down the dropped Cheerios to your stomach. Standing with not much success record, the "five second rule" is to keep dropped and dirty food from baby or kid. The basically says that a food piece dropped on the floor is bad (or done) after 5 seconds.

Five Tau (t) Rule

There is, by the way, a rule called (by me) "Five Tau (t) Rule." What it says is similar to the 5 second rule: A transient event (expressed usually in terms of current) dies down after five Tau seconds. In other words, a transition from a (steady) state to another (steady) state lasts only for five Tau seconds. For example, a switching off source from an R-C circuit and thus the change in the current amount flowing in the R-C circuit from a certain level to zero takes five Tau seconds. If Tau is 1, then the transition takes 5 seconds. It would be 5 micro-second if Tau is 1 millionth. What determines the Tau? The circuit. More specifically the values of R and C in R-C circuit, or R and L in R-L circuit.

Tau Dynamics

What the heck is Tau (t) then? Tau is as discussed above "time constant" as the name implies it's a constant (or fixed) about time. It's a constant determined by the values of R and C, or R and L. And it is about how long or short the transition would be. In an R-C circuit, Tau is calculated as 1/(R*C); in R-L circuit, it is L/R. The transitional current is usually expressed by an exponential equation which has a term containing EXP[-t/t]. Now consider the numerical values of the exponent as we change the time, t. When t=0 in other at the exact moment of the switching off, the exponent (or the relative value of the transient current) is EXP[-0/t]=EXP[-0]=1. When t=1t, EXP[-t/t]=EXP[-t/t]=EXP[-1]=0.3678. In other words, after 1t second (whatever value the t may be) the current is reduced to 36 percent of the initial value. Let's go further down the road. When time elapses 2t, the current now is EXP[-2t/t]=EXP[-2]=0.1353, that is 13 percent of the starting value. When elapses to t=5t, the current now lays at, EXP[-5t/t]=EXP[-5]=0.00673, that is less than 1 percent. As you see here, the value never reduces to zero, at least is theory. In practice, we have to compromise to say that a certain value is zero enough to be qualified to be zero. The consensus reaches at the value less than 1 % of the starting value at which t=5t. The birth of the 5 Tau rule!

Practical Wisdom

As I explained above, in an R-C circuit, t= 1/(R*C). You know what? In a circuit, R is a power consumer. If R gets bigger, t becomes smaller, and the transition time to zero gets quicker. Assume that your dad wired you $1000 into your bank account. How long the balance floats above zero is determined by how big your spending (consumption) desire (not need) is. Unlike in most circuit applicatins, my advice on t in the life-time application is: Choose a long one.

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