# Battery Electronics 101

Performance of electric vehicles, solar power, wind power generators and similar alternative energy power systems is determined by their electrical systems.

Low cost, easy-to-use tools like the "Watt's Up Watt meter" give you the ability to understand, modify and troubleshoot your power systems for best performance.

Below are some questions and answers that may help you better understand and utilize your test equipment.

- How to convert mAh to Joules?
- What's the difference between an Ah and a Wh?
- Will a larger battery make my vehicle faster?
- How do wiring and connectors affect performance?
- Why must I use connectors designed for high current?
- What's the difference between
*continuous*and*intermittent*current measurement specifications?

## How to convert mAh to Joules

Since an Amp Hour (Ah) is a measure of **charge** (measured in "Coulombs") whereas a Joule is a measure of **energy**, you can't convert mAh to Joules without first knowing the voltage (Volts) a which the charge was transferred.

Given that voltage the conversion is just:

**Charge (C) x Voltage (V) = Energy (J) **

and,

**Current (A) x time (seconds) = Charge (C)**

To find the mAh to Joule conversion we first find the charge in a mAh.

mA means 1/1000 of an Amp for an hour and there are 60 x 60 = 3600 seconds per hour. So,

1mAh = 0.001 Amps x 3600 seconds = 3.6 Coulombs of charge.

Choosing 1 Volts for the voltage, we can now convert mAh to Joules.

**3.6 (C) x 1 (V) = 3.6 (J)**

We say at 1 Volts, 1mAh of charge equals 3.6 Joules of energy. This is a handy value for mAh to Joule conversions.

**For any voltage, mAh X voltage x 3.6 = Joules of energy.**

For example. A 7.2 Volt battery that delivers 100 mAh of charge has delivered,

100 x 7.2 x 3.6 = 2592 Joules of energy.

As we saw above, since a mAh is 1/1000 of an Ah, **to convert Ah (amp hours) to Joules** just use 1000 x 3.6 = 3600 as the conversion factor instead of 3.6.

## What's the difference between an Ah and a Wh?

An Amp Hour (Ah) is a measure of **charge** (measured in "Coulombs") whereas a Watt Hour (Wh) is a measure of **energy**. The two are related by **voltage**. So a 36 V battery stores twice the energy (Wh) of an 18 V battery.

When only an Ah specification is given it is understood that the voltage that determines the energy this represents is that of the battery (storage device).

In summary, the energy (measured in "Joules") stored in a **36 V, 15 Ah (15,000 mAh) battery** is 36x15= 540 "Volt-Amp-hours" or Watt - hours. Where a Volt-Amp-hour (Wh) is 3600 Joules (J). So **our battery has stored 1,944,000 Joules** of energy!

That's **pretty close to** the ~2,110,000 Joules in **a stick of dynamite**? A good reason to respect storage batteries!

## Will a larger battery make my vehicle faster?

A larger (bigger or higher Amp hour capacity) battery with the same open circuit voltage will make your vehicle faster **only** if it has lower internal series resistance and can, therefore, deliver more current to the same resistance load. e.g. your motor.

Think about it using a bucket of water analogy. A fixed diameter hole (resistance), a fixed depth (voltage) below the surface, will leak water at the same rate (current) for any diameter (e.g. capacity) of bucket.

## How do wiring and connectors affect performance?

Though it's typically very low (only fractions of an Ohm), wires and connectors do have resistance.

Consider a 24 V battery pack with a motor that draws 25 Amps. We measure only 22.5 Volts across the motor. The rest is lost on the wiring and connectors. Ohms law tells us they have (24-22.5) = 1.5/25 = 0.06 Ohms of resistance.

Lets say we can reduce their contribution 5X to 0.012 ohms. The voltage drop in the wiring is now 5 times lower. Ohm's law again, V= I*R => 25 x 0.012 = 0.3 Volts.Power (Watts) = V x A => 0.3 x 25 = 7.5 Watts lost in the wiring and connectors compared to the 1.5 x 25 = 37.5 W we started with.

In reality the motor current and speed would go up because of the increased voltage, but the fraction of power going into your motor has gone up too and that's the goal.

So using fat wires and low resistance connectors can pay off. Your motor gets more voltage and less of your battery's energy is going into heating your connectors and wires!

## Why must I use connectors designed for high current ?

Like the wires they connect, connectors have resistance that's measured in Ohms. That resistance depends on the type of metals making contact and the total contact area. Other things being equal, increasing the contact pressure (from crimping or spring tension) maximizes contact surface area and thus lowers resistance.

Another benefit of higher contact pressure is reduced vibration induced (fretting) corrosion. This is because the increased pressure reduces the relative motion between the contact faces and that motion tends to create metal oxides that increase contact resistance. Properly designed noble metal contacts (e.g. Gold plated over Nickel) or contacts with a contact lubricant (e.g. our AX7) minimize fretting corrosion. Increased contact resistance creates positive thermal feedback that heats and destroys contacts.

Here's an example. A contact having a resistance of 0.015 Ohms and 35 Amps current through it means that contact must dissipate (P=I^2 x R) 35 x 35 x 0.015 = 18.4 Watts of power! The thermal insulation of heat shrink tubing, and being buried in your equipment gives you the equivalent of a small soldering iron getting pretty hot.

Unlike wires, a contact's resistance is developed over the tiny area that actually makes contact between the mating connectors. In a contact all that generated heat is dissipated over that tiny area rather than the whole bulk of a wire.

The heat increases the contact's resistance (since a metal's reduced stiffness at temperature reduces contact pressure) and more power in the system goes into the contact until something bad happens.

Note that the squared relationship of current to power dissipation in resistance means things change fast at higher currents. E.g., at 49 amps the contact is dissipating 36 Watts! The current in your circuit "I" is the voltage divided by total resistance. e.g. I=V/R. (in Amps, Volts and Ohms). If your contact resistance increases, some of your battery voltage is now wasted across your contacts instead of going to your motor and its speed control. Your maximum current is less because there's more total resistance (assuming the motor control is wide open). What gets lost is Power.

If you measure the Amps through and Volts across your connector you can find its resistance (Ohms) and power dissipation (Watts) and know Watt's what (sorry).

Yes, a "Watt meter" that can measure down to 0 volts like our "Watt's Up" meter will be a handy tool for testing these things. Armed with the above, you can measure just what your situation is and verify it isn't degrading over time.

## What's the difference between *continuous* and *intermittent* current measurement specifications?

Specifying a parameter, e.g. current, as continuous means you can expect the device to handle it, well..., continuously. That means it shouldn't be damaged by operating at that amount. A parameter not obviously specified as continuous **may not be!** Convention may expect it to be so (e.g. a household light bulb has a continuous voltage rating that's unstated), but you should check it as failure to be so rated could cause damage or error if used continuously.

Intermittent ratings, ideally, have a time or *duty cycle* associated with them. E.g. 100 Amps of current for 20 s per minute means the device should handle 100 Amps for a total of 20 seconds in any 60 second interval. That is also called a 33% duty cycle over a minute because the device can handle the rated amount for 20/60 = one third or 33 percent of the minute.

Here's an example. When high currents flow in wires, their electrical resistance produces heat. That's how an incandescent light bulb filament works. A test device like a Watt meter may produce 10 Watts of heating with 100 Amps running through it due to its internal resistance. That's like a small soldering iron. If on for a few seconds it would barely warm up. But after 10 minutes it might have melted the case! So it might have an *intermittent* rating of 100 Amps for say one minute in any ten or a 10% duty cycle over ten minutes. That same Watt meter might be able to continuously handle 20 amps corresponding to 0.4 Watts of heating *continuously*.

While we have discussed current, continuous versus intermittent ratings are relevant for many specified parameters. Other examples are: voltage, temperature, pressure, acidity and duration of a baby crying.