# The Incorrect Application of the Concept of Average Current.

Our grade school and high school teachers try to teach us that 20 amp for 1/2 of a second out of each second is the same as 10 amps continuosly for 1 second.

Well…. like many other things that public school teachers told us, that is only true *sometimes*.

Let’s take an example connector rated for 10 ampere continuous. This connector is rated for 10 ampere DC or 10 ampere rms AC.

When a connector is rated “10 amp continuous” that should mean that we can safely run 10 amp DC or 10 amp AC forever without overheating it.

Can you use this connector for a circuit that runs 20 ampere at 50% duty cycle? Or perhaps 40 ampere at 25% duty cycle?

An ampere is 1 coulomb of electrons per second. So running 20 amp (20 coulomb per second) for 1/2 of a second, and then no current for 1/2 of a second, we still have 10 coulomb of electron moving in one second. Isn’t that the same as 10 amp (10 coulomb per second) for a whole second? That is 10 coulombs moved in 1 second, so why isn’t it the same?

Lets consider what it is that limits a connector’s current carrying capacity; resistance! Resistance between the wire and the female crimped contact, resistance between the female contact and the male contact, and resistance between the male contact and the next wire. These will all create heat from the current flowing through them.

For the purpose of this article, we will consider only the resistance between the female and male contacts. If the contacts were properly crimped to the proper size wire, the inter-contact resistance will be much greater than the resistance between contacts and wire, so we can ignore the latter.

Looking at the specification sheet, we can see that a typical ‘high current’ connector will have a maxium resistance of 3 mohms when properly assembled and mated, and at its rated operating temperature.

The heat created at the contact interface is easily calculated as I^{2}*r. At 10 ampere this will be 10 * 10 * 0.003 which is 100 * 0.003 = 300 milliwatt. 300 milliwatt is 300 millijoule each second.

Watt is *rate* of energy flow. Joule is a unit of energy. 1 watt is 1 joule per second.

What happens at 20 ampere, but 50% duty cycle? (Continually repeat the pattern of 20 amp for 1/2 second, 0 amp for 1/2 second.) During the 0 current half of the second, heat generated will of course be 0. During the other half of a second, using I^{2}*r, the rate of heat generated will be 20 * 20 * 0.003 which is 1.2 watt (during the half second while carrying current.) That is a *rate* of 1200 millijoule per second, but only for 1/2 of a second each second which solves to 600 mJ each second. That is twice the heat the connector is rated for.

Now lets look at 40 ampere at 25% duty cycle. The average of 25% duty cycle of 40 amp is 10 amp, so can’t the connector safely carry this current? Again, using I^{2}*r, we will solve for the rate of heat generation. 40 * 40 * 0.003. This solves to a rate of 4.8 joule per second, but at 25% duty cycle, we find that heat per second is 4.8 * 25% = 1200 mJ per second.

That is *4 times the rate of heat generation* from the rated 10 ampere continuous condition.

Perhaps 1200 mJ per second does not sound like much to you. After all, my counter top bread toaster is 900 watt. Have you ever grabbed a 1 watt resistor? All of us ‘old timers’ that worked on tube equipment have, and let me assure you 1 watt can burn your skin.

If we continue to run this 40 ampere at 25% duty cycle, the temperature of the contacts will rapidly rise quite high. And with higher temperature comes higher resistance. With higher resistance we have more heat generated which raises resistance and so on until the connector fails.

So when choosing a connector for your next design, be sure to read the entire specification sheet.

Until next time, happy soldering!