I = V/R
Current equals voltage divided by resistance.
R = V/I
Resistance equals voltage divided by current.
With this law, if you know any two of the variables, you
can solve for the third unknown variable. This comes in
handy when, for instance, you want to specify the resistor
for an LED. Let’s say that you will be powering at 3.3V and
the datasheet says the LED is most efficient when passing
15 mA of current. You solve the resistance formula:
R = V/I
R = 3.3/.015
R = 220 Ω
Since 220 Ω is a standard resistor size, we can easily
get the exact resistor needed. If we use 1K Ω resistors and
have 5V power, the current can be found with:
I = V/R
I = 5/1000
I = 0.005 amps
While 5 mA (0.005 amps) is under-powering the LED, it
is plenty bright. Since we may be using batteries, the lower
current saves power and extends the battery life.
Circuits
We get electricity to do useful work by channeling it
from devices that produce electric force (like generators
and batteries), through devices that do electric work (like
lights and motors), and then back to the device that created
the force. That last part is critical. Circuit is just a fancy way
of saying ‘circle.’ Electricity must run in a circle to be useful.
Figure 3 shows arrows marking the direction of
conventional current from the higher voltage side of a nine
volt battery (the positive terminal) through a resistor and an
LED, back around to the lower voltage terminal of the
battery. You’ve probably seen complex circuits on printed
circuit board (PCBs) or as schematics, but no matter how
complex it looks it can be simplified to: one part producing
the force as a current; one part using that force to do work;
and the circular electrical connection between them.
Short Circuits
If we connect a copper wire between the + and –
terminals of a battery — ‘short circuiting’ them (as shown in
Figure 4) — the current will rush through, doing a lot of
work making the wire heat up and quickly depleting the
chemicals in the battery that are creating the electric
potential difference in the first place.
Don’t try this experiment because not only will it
deplete your battery, many batteries will heat up and
possibly even explode when treated this way.
If you are doing Arduino experiments plugged into the
USB port of your computer, you are using +5V supplied
from the PC over the USB cable. If you short-circuit the + to
the - (and if you are lucky), the USB protection circuits on
the PC will detect the current rush and shut down your
USB connection before something blows up. If you aren’t
lucky? Well, say bye bye to something expensive. The
morale? Be careful not to short-circuit anything expensive,
flammable, or with tendencies to explode — including you.
Voltage Across Resistance
Let’s build a circuit that lets us play with Ohm’s Law.
We put eight 1K Ω resistors on a breadboard so that they
are each connected in series; this yields 8K Ω in 1K Ω
increments. Connect one end of this series to +5V and the
other end to the GND as shown in Figures 5, 6, and 7 that
show the current and the voltage drop across this circuit.
This arrangement of resistors is called a voltage divider
and allows us to access each cumulative resistance value
from 0 to 1K, 2K, 3K, 4K, 5K, 6K, 7K, and 8K. [The
illustrations also show the Arduino analog input pin 0
attached between the fifth and sixth resistors, counting up
from the +0V. We will look at that in a minute]. Let’s play
June 2014 61
■ FIGURE 3: Electric current
from battery through
resistor and LED.
■ FIGURE 4:
Short circuit.
