Car Audio Basics - Ohms Law

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 connections.

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 connections are not used as often as parallel connections because they reduce power.  However, they are easier for your amp to drive since they draw less current.

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 connections 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.

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