IT = CV …or what I never learned in tech school

IT = CV is a very basic and useful relationship that all electronics students should master. It is akin to Ohm’s Law, but something I was never taught in tech school –I had to learn it myself much later –now I use it at least weekly. Every electronics instructor should get a hold on this one and make sure his students get this simple concept –perhaps some already teach this –if so, good for them.

The problem with tech schools

Excellent professors are few and far between and my tech school, even though highly rated, typified this shortcoming. The problem, I believe, is that many engineers who do not fare well in industry find a home in academia where they perpetuate mediocrity –and these are definitely not ‘circuit-heads.’ My hat goes off to those bright instructors who truly teach, inspire and bring out the best in their students, but I recall only a few that even came close –in my case, these excelled at conveying absolute truth and dispelling abundant electronic misconceptions.

The problem with coulombs

We have all touched upon this unit of electrical charge, but at best it is simply an obscure unit of measure –while we may understand the concept, we simply do no not think in coulombs. We think in volts, amps, ohms and seconds, but not coulombs –it is simply too intangible.

An important equality

Q = C * V Where Q = charge in coulombs, C = capacitance in farads, and V = volts.

Q = I * T Where Q = charge in coulombs, I = current in amps, and T = time in seconds.
…perhaps better defined as amp-seconds…

Therefore: IT = CV (Note that the unit of charge has disappeared.)

Solving for the four specific variables

I (in amps) = CV /T (here, it represents a fixed current flow –a current source)

T (in seconds) = CV /I (here, it represents an elapsed time of change in time)

C (in farads) = IT /V (here, it represents a fixed value)

V (in volts) = IT /C (here, it represents a change in voltage)

What is a voltage source?

Most understand this –it is a voltage that is essentially unchanged over a range of load currents.
Common examples include batteries or fixed voltage power supplies.

What is a current source?

A current source is a little more mysterious and less understood –it is a current flow that is essentially unchanged over a range of load voltages.

Examples include a current-limited power supply, constant current diode, a photo-voltaic solar panel, diode leakage, or the input current to an op amp integrator. (I, myself, use a current limited power supply to simulate solar panels.)

Most simply, it may be defined as the current flowing through a fixed resistor when a fixed voltage is placed across it.

Examples of how this is applied

1. If 1amp flows into a 2000uf capacitor for 2seconds, what is the voltage developed?

V = IT /C = 1A * 2sec /0.002Farad = 1000V

2. How much capacitance is required to limit its voltage change to 1V when the capacitor discharge current is 100mA and the elapsed time is 8.33mS?

C = IT /V = 0.1A * 0.00833sec / 1V = 0.000833farads = 833uf

3. If a leakage current charges a 0.47uf capacitor to 3V in 60sec, what is the leakage current?

I = CV /T = 0.47E-6farads * 3V /60sec = 2.35E-8A = 0.0235uA

4. If a charging current of 100uA is applied to a 0.1uf capacitor, how long does it take to charge to 8V?

T = CV /I = 0.1E-6 * 8V /100E-6A = 8E-3 = 8mS

The real world

Unfortunately, in the real world, currents are rarely constant. However, approximations are often quite accurate if the current does not vary more than roughly 2:1. In the following case, it is simply averaged.

Problem: Ignoring normal design rules, calculate the approximate frequency of this TLC555 astable oscillator, then compare with experimental measurements.

R1 = 100K ±1%, C1 = 0.1uf ±1%, Vcc = 12V
Vthesh low = 4V, Vthresh high = 8V

First, determine average capacitor charge /discharge current
Iavg = (12V — Vavg) /100K = 6V /100K = 60uA

Second, determine charge period between the two thresholds (4 to 8V)
T = CV /I = 0.1E-6uf * 4V /60E-6 = 6.66E-3 = 6.66mS

Since this is half of the full cycle period, the full cycle = 2 * 6.66mS = 13.33mS

F = 1 /period = 1 /13.33mS = 75HZ

Measured frequency = 71.84HZ

Accuracy = (71.84 – 75) / 75 = -0.042 = -4.2% (not bad for an approximation…)

Note that the math could be further manipulated to eliminate the voltage as its effect in this case cancels out.

Schematic

Oscillographs

Photos

Undocumented words and phrases (for our ESL friends)

circuit-head –idiom that I coined –someone who eats, drinks and sleeps circuits –akin to the more commonly used ‘motor-head’ idiom that aptly describes those who eat, drink and sleep engines and fast cars…

what happens when time becomes infinite???

i=cv/t

i= (0.000001 * 12)/(1/0) = 0 amperes

• mista

>> what happens when time becomes infinite???

tl;dr; It won’t! Really NOT! Trust me, I’d happily bet not just my humble life on that, but even the mere existence of our whole universe.

Well, lots of highly interesting, very strange things might have happened for an eternity!

BUT – who cares, as you & me (as well as any imaginable mortal sentient being) will already be dead and rotten for almost eternity;

AND it’ll be so [edited] cold with all the universe being in thermodynamic equilibrium by then, at a temperature just marginally above absolute zero;

AND it’ll be really a very, very boring phase, as the very last event that then has happened will be about an eternity ago; just imagine how boring a day, or even just an hour can get, if absolutely nothing is happening; and now think of that non-happening extended for an eternity – so absolutely boring!

AND since entropy will then have reached it’s absolute maximum at about infinity, I can tell you for sure, that nothing will happen for at least the next infinite number of eternities.

Finally when all the above will have happened, it’ll still be an almost indefinite number of millennia (or seconds) before time becomes infinite!

[Edited language]

• William Morrison

Doesn’t matter if t=infinite!

After about 5 time constants the cap is fully charged and current drops to Zero.

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