# Ohms Law, as it pertains to the Musician

1/04, updated 7/05 - Jens Moller http://www.colomar.com/Shavano/ohms_law.html

NOTE: This is one subject area that you will need a cursory knowledge of math to use. Any calculator that can handle square roots should simplify the usage quite a bit.

E (Voltage) and P (Wattage) use their RMS values.

Many people ask me about changing around an amplifiers speaker wiring - either by adding more speakers or connecting them in different ways. A lot of things happen when speaker loading changes, and if you know how Ohms Law works, it will simplify your design efforts quite a bit.

I always refer to the documentation that came with any amplifier, especially as it pertains to loading/speaker Impedances.

### What does Ohms Law help us do?

Often we want to know how much power something has, or it will have when we have reconfigured it. If we know at least 2 things (any of Watts, Amps, Ohms or Volts), we can figure out the other 2 things. The Ohms Law chart has a center ring containing 4 items (P, I, R and E) and then an outer ring that contains equations that relate to finding out the values of the inner 4 items. This chart is color coded to simplify its use - all the like colors work together.

Our focus will be on using this for working out things that musicans care about, and nothing very esoteric, so I'll avoid any details that really are not important to our needs.

Ohms Law operates assuming a perfect world - the issue is that nothing is truely perfect and Ohms Law does not account for losses or design limitations that we may not be totally aware of. We can, however, use it to create some generalizations that tell us a whole lot about the cause and effects of our power usage.

### Common Examples

• How do I figure out how much power is going to my speakers?

Or

Why is it not louder when I add more speakers (it often isn't)?

If your amplifier is rated at 100 watts at 8 ohms, we can solve for E (voltage) by looking at the Blue area and find an equation that uses both P (watts) and R (ohms) - We see that to get this voltage level, we have to multiply P x R, and then take the Square Root of that value. In this case:

```    P (Watts) = 100
R (Ohms) = 8

P x R = 800

The Square Root of 800 is approx 28.3

So, with an 8 Ohm load at 100 Watts, the speaker will see up to 28.3 Volts (E = Volts)
```

Now, if we want to add another 8 Ohm speaker in parallel, that would change our impedance to 4 Ohms (2 8 Ohm Speakers in parallel = a 4 ohm Load), what would the power to the speakers become? For this, we needed to know the voltage that we had for 100 Watts at 8 Ohms. Why? Because the power supply in the Power amp is limited to how much voltage it can give us. We know that this value from working out the above. To find out our wattage change, we look at the P (Power) inner circle, and the RED equations.

```   R (Ohms) = 4
E (Volts) = 28.3

E squared / R will tell us what we want

28.3 squared is approximately 800
800 divided by 4 = 200

So, if we increase the load of the amplifier from 8 ohms to 4 ohms, we should see more power,
and in this case, its 200 Watts. As long as the power supply can provide 200 watts, we will
have doubled the available power.
```

What happens if I put the 8 Ohm speakers in series, effectively giving me a 16 Ohm load? the equation to use is the same, we simply plug in a different value for R.

```   R (Ohms) = 16
E (Volts) = 28.3

E squared x R will tell us what we want

28.3 squared is approximately 800
800 divided by 16 = 50

So, if we reduce the load of the amplifier from 8 ohms to 16 ohms, we should see less power,
and in this case, its 50 Watts. If the power supply can provide 100 watts, it can easily handle
50 watts and we have halved the available power.
```

There is an effect here that is not obvious until you look at the numbers. Running things in parallel and using the lowest impedance load possible gives you the most power. In the case of running 2 8 Ohm speakers in parallel - you'll see in our example that each gets to split the 200 Watts between them - in this case, each speaker sees 100 Watts, which is the same Power that the individual 8 Ohm speaker saw when it was the only load on the system. In the case of running things in series, a more dramatic change occurred:

• First, the available power dropped by 50%,
• Second, the available power that is split between the speakers is 1/2 of the available power, and in our example, these speakers now only see 25 watts each. Thats 1/4 the amount of power that the individual speaker had if run by itself at 8 ohms or when 2 are run in parallel giving a 4 ohm load.

All this implies that if we simply keep putting more and more speakers in parallel, we get more power. This is true until we hit the limit of the Amplifiers internal Power Supply - the current (I) that it can give us, or the current (I) that the Power Amp output stage is limited to. Heat plays a big part in this - when anything gets hot, some of the power that was supposed to drive the speakers is lost. The hotter it gets, the bigger the losses. Too much heat and the Audio Output stage fails (often this occurs quickly and catostropically. The most common failure mode I run into seems to favor dead shorts in the output Power Transistors, which dumps raw voltage into the speakers, and frequently burns up the voice coils in a matter of seconds). These are strong arguments for not placing too high (lower impedance) of a load on any power amp.

Always refer to the documentation that came with the power amp to see what Impedance is recomended. 8 ohm support is common. 4 ohm is also common, but not as common as 8 ohm. 2 ohm is rarely supported, however some amplifiers can handle it (please check before trying it).

• ### How do I know how much power my equipment is using

This can be critical when you are dragging out extension cords to hook up all your gear with. You will need to avoid drawing more power than is available. If you know the Power (Watts) ratings of all the gear you want to hook up and what the E (Voltage) is, then you can estimate I (Current) draw.

In the USA, most homes are wired for 15 amps per circuit. Some power outlets are good for 20 amps, but its not good to assume you have more than 15 amps available. Most often you end up sharing your power source with other things, such as lighting or kitchen devices. Because you don't know whats out there competing with your gear, its usually not a good idea to draw more than 10 amps - this allows for 5 amps to be used by anything already connected up to the same power source. Looking at the Ohms Law chart, you can see that if you add up the Wattages (P) of all the devices you plan to use, and divide that by the Voltage (E), you will get the Current needed (I).

NOTE: We do not work on Home or Car Audio. We work only with Pro-Audio applications. We cannot help you with Home or Car Audio questions.