Okay, time to get up on the soapbox again. It's probably my three quarters electrical engineering circuit analysis education, but why can't most newbie sound people figure out how much power, voltage and current is going into each of their speakers? I mean Ohm's Law and Watt's Law have been around since before Thomas Edison invented the light bulb, Edison sockets (for the light bulbs) and Edison receptacles (for plugging things into). So I guess it is time we had a refresher course on the basic electrical formulas, and those of you who know this stuff can guess the famous dead physicist's names that make up the laws. Ohm's Law
Georg Simon Ohm (1789 – 1854) had his name bestowed as a unit of electrical impedance (resistance) and generally denoted as Z (for impedance) or R (for resistance). Ohm's Law is defined as volts divided by amperes to equal ohms (R = V/I). For those of you quick with your algebra, you can solve for volts (V = I x R) or amperes (I = V/R); knowing two out of the three solves the third.
As an example, an eight ohm speaker with 100 volts of audio signal has 100/8 amperes, or 12.5 amperes, running through the positive and negative wiring. And if you were foolish enough to plug your speaker directly into a 120VAC receptacle, you would have 120/8 or 15 amperes of current–that's not enough to blow a household circuit breaker, but is enough to make your speaker turn into a smelly fuse or a large electric match.
The physicist Alessandro Giuseppe Antonio Volta (1745 – 1827) got his name attached to electrical potential or "volts". Mr Volta is famous for inventing the first voltaic pile or "battery". Andre-Marie Ampere (1775 – 1836) is forever attached to electrical current flow as amperes, or "amps" for us modern-day electrical heathens. The way you should envision electricity is to imagine a garden hose with the water pressure as volts and the amount of water flowing per second out of the hose-end as amperes. Thus the diameter of the hose can be thought of as impedance. The bigger the hose, the lower the impediment (impedance) to large water flows.
Watt's Law
Shifting that analogy to power, the amount of water per second (amperes) and the exit water pressure (volts) creates a force that does work which is defined as "power," if averaged on a per second basis. English physicist James Watt (1736 –1819) had his name attached as a standard unit of power, besides inventing a practical steam engine. Otherwise we would still be equating our speaker power-handling in horsepower (746 watts per horsepower).
Watt's Law states that voltage (V) multiplied by current (I) equals power (P). So in our 100 volts into an eight-ohm speaker example, the Ohm's Law result provides 12.5 amperes, or 100 times 12.5, or 1250 watts of audio power via Watts Law. And for you algebra nerds, you will quickly resolve the companion equations of V = P/I and I = P/V. And the real algebra terrorists will solve all the combination Ohm's and Watt's Laws with resistance as well. These are:
Test Your Knowledge
Now every power amplifier does not have a proportional change in power-out with the change in applied speaker load resistance, but most manufacturers do list power ratings for four-ohms and eight-ohm nominal loads. In Figure One, I show two eight-ohm speakers chained together for a parallel load of fourohm applied to the power amplifier. In this example figure, I show the amplifier providing 1100 watts at four ohms. But many amplifiers of this rating are likely to provide 600 or 700 watts of power into an eight ohm speaker load. So as you load the channels with paralleled speakers, each speaker does not have independent power, but the total speaker load interacts with the amplifiers' ability to give each speaker audio power. The lesson here is to buy more amplifier channels if every watt counts.
So regardless of the speaker cabinet's actual power handling ratings, the example wiring in Figure One shows the 1100 watts being evenly divided into the two speakers. This is important, as most newbies think there is 1100 watts going into each speaker, or that 1100 watts comes out of the amplifier regardless of the speakers connected. Each speaker's load impedance sets the amount of possible power the amplifier can deliver to that load, considering the total loading.
Running through the math, we know that two eight-ohm speakers parallel wired is four-ohms at the output connectors of the amplifier. Using Watt's and Ohm's Laws, 1100 watts into four ohms is 66.3 volts (V = sqrt(P x R) = sqrt(4400)). Using Ohm's Law, the amp to first speaker current is 16.6 amperes (I = V/R = 66.3/4). But the second speaker cable patching from the first speaker's jackplate will only pass half the current or 8.3 amperes into eight ohms for the 550 watts (P = I2 x R = 8.32 x 8) using the combo of Watt's and Ohms' Laws. Note that I show red arrows on the figure that depict the conditions as if I were measuring parameters into the loads.
Extra Credit–More Dead Physicists
I hope my brief run through all that math clarified things a bit. For those not getting it completely, there are pretty of circuit analysis textbooks available that show the laws, formula and theorems necessary to break complex loading into useful results. I intentionally skipped over AC versus DC descriptions of volts, amperes and watts as that only messes up people trying to get the basics mastered.
And we still have room for some more physicists. For AC circuits, one must pay homage to Heinrich Rudolf Hertz (1857 – 1894), the man who discovered "Hertzian Waves" that we generalize to alternating currents. And then there is Michael Faraday (1791 – 1862) and Joseph Henry (1797 – 1878) whose capacitors and inductors are now measured in farads and henries respectively. And one can not measure energy (power times seconds) without thinking of James Prescott Joule (1818 -1889), and the joule's equivalent of watts times seconds. An electric charge must be measured in coulombs instead of amperes times seconds (or farads times voltage) thanks to fellow physicists voting Charles-Augustin de Coulomb to represent that unit.
Just remember that these famous physicists have metric system surnames like femto- nanomicro- milli- deci- hecto- kilo- and mega-. This is so you can understand your nano-farads from your kilo-watts.
