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Understanding Ohm's Law
Understanding Ohm's Law
Understanding what ohms are and how they relate to
car audio is most helpful when trying to determine optimal wiring configurations
for connecting multiple speakers to an amp. There are some basic
electrical engineering formulas I will use on this page. Fortunately they
are fairly simple.
Ohm's law: Current = Voltage /
Resistance or I = V / R
You can rearrange this formula in a couple ways: V = I *
R and R = V / I
Power equation: Power = Voltage^2 / Resistance or P = V^2 / R
Rearranging this formula gives us: R = V^2 / P and V = SQRT(P * R)
Using Ohm's law we can derive some more power equations: P = I^2 * R
Rearranging gives us: I = SQRT(P / R)
Abbreviations used on this page are:
I : current, measured in amps
V: voltage, measured in volts
R: resistance, measured in ohms
P: power, measured in watts
With that out of the way we can get down to business.
As stated earlier, ohms are a measure of electrical resistance.
It helps in this discussion if we consider amplifiers to be perfect voltage sources.
Consider this 25 watt amp:
P = V^2 / R
Most amps are rated into 4 ohm loads so we now have:
25 watts = V^2 / 4 ohms
Solving for voltage we get: V = SQRT(25 * 4) = 10 volts
So our 25 watt amp can be considered here to have the ability to produce up to 10 volts output.
Now let us consider what happens when we connect two speakers
in parallel to the amp. At this point I am going to introduce some more
formulas. We are considering speakers to just be simple 4 ohm resistors
for this discussion. There are formulas which dictate what happens when
you combine resistors in various ways. Before that we need to explain what
is meant by parallel and series ConneXions.
Each channel of an amplifier has a positive (+) and negative
() connection. The amp develops a voltage between these two terminals and
this voltage is what drives the speakers. The equivalent resistance of
what you connect to the amp is referred to as the load.
Normally when connecting a single speaker to a single amp
channel you merely connect the "+" terminal of the speaker to the "+" terminal
of the amp. Then do the same thing for the "" terminals. Things get
more complicated when you are connecting multiple speakers to a single amp
channel. In a parallel configuration you connect both "+" terminals of the speakers to
the "+" terminal of the amp. Then do the same thing for the ""
terminals.
A series connection is a little more complicated.
First, you connect the "+" terminal of the amp to the "+"
terminal of one of the speakers (let us call it speaker A). The next thing
you do is connect the "" terminal of speaker A to the "+" terminal of the other
speaker (speaker B). Lastly, you connect the "" terminal of speaker B to
the "" terminal of the amp. You can see in this connection that power
from the amp goes through both speakers one after the other, hence the name
"series."
Finally, here are the formulas that tell
you what resistance load you end up with when wiring multiple
speakers:
For two speakers in parallel:
1 / Rt = 1 / Ra + 1 / Rb
where Rt is the total equivalent resistance
or load and Ra and Rb are the resistances of the two speakers. You can see
that you can use speakers of different resistances but there other implications
of doing that which are usually undesirable because the power will not be spread
evenly between the speakers.
Working through the math if you put two 4
ohm speakers in parallel you get:
1 / Rt = 1 / 4 + 1 / 4
= 1 / 2, Rt = 2 ohms
The equivalent resistance is exactly half
of what we started with. We will look at the implications of this a little
later. Let us do another example first with three 4 ohm speakers in
parallel:
1 / Rt = 1 / 4 + 1 / 4 +
1 / 4 = 3 / 4, Rt = 4 /3 = 1.33 ohms
You can see that as you put more and more
speakers in parallel the equivalent resistance will drop further.
Next lets look at the equivalent resistance
for speakers in series:
Rt = Ra + Rb
Now that is easy! You just add the
resistances for each speaker so putting two 4 ohm speakers in series will you
give a single load of 8 ohms.
With that background out of the way we can look at what effect
these different wiring combinations have on the amplifier. Going back our
25 watt (10 volt) amplifier with a single 4 ohm speaker we have:
Current = Voltage / Resistance = 10 / 4 = 2.5 amps
So when this amp is producing maximum power (25 watts) into a 4
ohm load, the load will draw 2.5 amps from the amp.
Now let us look at what happens when we connect two 4 ohm
speakers in parallel (which gives us a 2 ohm equivalent load) to this
amp:
Power = Voltage^2 / Resistance = 10^2 / 2 = 50 watts
This is seems great! Our 25 watt amp
is now producing 50 watts but there are some complications. Let us see the
current now:
Current = Voltage / Resistance = 10 / 2 = 5
amps
Even though our voltage is still the same
(10 volts) our current has now doubled from 2.5 amps to 5 amps. If the amp
has the capability to produce this much current and dissipate the heat that this
will generate then everything will be fine. One way to determine if your
amp is capable of this is to look for power ratings that are given into 2 ohms
in addition to the normal 4 ohm rating. Further if the power doubles into
the 2 ohm rating then the amp has ample current capacity. Another clue to
tell whether the amp will work with 2 ohm loads is look for the phrase "2 ohm
stable." Being 2 ohm stable only means that the amp will function with 2
ohm loads; it does not necessarily mean that the amp will produce more power
into 2 ohms. If you attempt to use a 2 ohm load with an amp that cannot
handle it a well designed amp will shut itself off or blow a fuse and a poor one
could be permanently damaged.
Next let us look at a series connection with two 4 ohm
speakers. This will give us an 8 ohm load and we will use our 25 watt (10
volt) amplifier again:
P = V^2 / R = 10^2 / 8 = 12.5 watts
Our amp is now producing only half its power rating! And
the current is:
I = V / R = 10 / 8 = 1.25 amps
The current is 1/2 its original value as well. Series
ConneXions are not used as often as parallel ConneXions because they reduce
power. However, they are easier for your amp to drive since they draw less
current.
Another option that is often available is to bridge an
amplifier. This process takes 2 amp channels and combines them to act as a
single more powerful amp channel. How to do this to an amp and wire
everything varies so please do not ask me how to bridge your amp. I can
explain the effects of it though.
What typically happens when you bridge an amp is that the
voltage it can produce doubles. Our 25 watt (10 volt) amp can now produce
20 volts. Let us look at how that affects power:
P = V^2 / R = 20^2 / 4 = 100 watts
This is 4 times the original power of the amp but let us look
at the current situation:
I = V / R = 20 / 4 = 5 amps
So now we see even with a regular 4 ohm load the current is
already double what the normal value (2.5 amps) was. For other reasons the
power usually does not usually quadruple when you bridge an amp but will
typically at least double. Connecting a 2 ohm load to a bridged amp raises
the current requirement even more. However, if your amp can handle it then
you will be squeezing a lot of power out of the amp.
In fact, many people use that kind of setup in competition
where the classes are judged by the power rating of the amps in the
system. A 25 watt amp can produce many times more power when bridged and
driving low resistance loads so the competitor gets more power than what appears
on the surface. Zapco and Phoenix Gold make amps which are able to drive
such low resistance loads (sometimes as low as 0.5 ohm!)
Some final notes:
 On this page I have considered amplifiers to be perfect
voltage sources. They are not though and they have some internal
resistance which lowers power output slightly.
 I have also considered speakers to be perfect 4 ohm
resistors. In actuality the resistance of the speaker depends on the
frequency the speaker is playing. For example, a speaker may have a 3
ohm resistance at 80 Hz and a 9 ohm resistance at 300 Hz. If you were to
make a plot of resistance versus frequency you would get what is called the
impedance curve of the speaker. Also, speakers act in some ways as
inductors and capacitors so a true model of a speaker must include those
components as well. How does this affect the sound you ask? Well
if you have an amp that has very weak current capability it may work fine into
perfect 4 ohm loads but when you connect our real speaker which has an
impedance dip at 80 Hz the amp may have difficulty and smear sounds that have
80 Hz components. These are minor but audible effects. This is why
it is good to get a 2 ohm stable amp even if you never plan on running 2 ohm
loads.
 Placing speakers in parallel and bridging amp channels are
effective methods for increasing the power in your system assuming your amp
can handle the increased demand.
 Use a series configuration when you need to raise the
effective resistance of the load. This occurs more often when you are
using dual voice coil speakers.
 Dual voice speakers have two speaker ConneXions on
them. This typically increases power handling capability and gives you
more wiring options. For example, if you have two dual 4 ohm voice coil
speakers you can get a single 4 ohm load which is suitable for connecting to a
bridged amp. You would do this by connecting the voice coils on each
speaker to each other in series. This would give you two 8 ohm
speakers. Next you put those two 8 ohm speakers in parallel and this
will give you a single 4 ohm equivalent load.
 Be aware that using lower resistance loads and bridging
produces a greater load on the amp. Well designed amps that cannot
handle the demand will either shut themselves off or blow a fuse. A
poorer designed amp can permanently damage itself. Also, even if an amp
works in these configurations it will probably generate more heat so
ventilation is even more important.
 As mentioned earlier ohms are a measure of electrical
resistance. You should be able to understand why resistance
changes affect the amp power as it does. If you raise the resistance the
amp is not able to drive as much current through the load and thus you get
less power. If you lower the resistance of the load math says that more
current will be drawn from the amp. Assuming the amp can handle this you
get more power.
 To understand why series and parallel configurations have
the effect on resistance that they do consider this. When you connect
speakers in series current must flow through both speakers and so it hits the
resistance of both speakers. When you have speakers in parallel, the
current has multiple paths since it can go through either speaker so the
equivalent resistance is always lower than that of either speaker
alone.




