# Electronics 101: Series and Parallel

April 19, 2012

Guest contributor: Rusty Wiseman

Hi folks. Welcome back to The Corner. This week we’re going to discuss the difference between series and parallel. I’m going to begin with a general description of what series and parallel are in terms of resistors and electrical circuits then I’ll talk about how this applies to guitar speakers and pickups/wiring configurations. There can be a lot of tech talk involved so I’ll try to keep this as easy to follow as possible for those that aren’t familiar with electrical circuits and hopefully provide a nice, clear explanation that people can use as a general reference when replacing speakers or pickups or rewiring cabs or guitars.

A series circuit is one in which the resistors are placed end-to-end such that the current only has one path to follow. A simple series circuit schematic is shown at right with the resistors denoted as R1, R2, and R3 (the jagged lines), the current denoted as the red capital I (the red arrow indicates the direction the current is flowing) and the voltage source denoted in green by the epsilon symbol and the two parallel lines.

In this configuration, the total resistance of the circuit can be found quite simply by the sum of the individual resistors. For example if R1 = 8 ohms, R2 = 4 Ohms, and R3 = 2 ohms then

Rt = R1 + R2 + R3

Rt = 8Ω + 4Ω + 2Ω

Rt = 14 Ω

The general formula for this is:

Rt = ∑ Ri

Since the resistors in this circuit are placed end-to-end and the current only has one path, this means that the current (I) is the same through each resistor.

It = I1 = I2 = I3

Also, the voltage across each resistor must add up to the voltage originally provided by the power source in the beginning so:

Vt = V1 + V2 + V3

Where V1, V2, and V3 denote the voltage drop across R1, R2, and R3 respectively.

A parallel circuit is one in which the resistors branch out from a spot called a node and rejoin again later in the circuit. You could also think of them as having their “heads” connected together and their “tails” connected together. Since resistors are non-polarized, it doesn’t matter which is which in terms of a simple electrical circuit such as the one shown below but when we talk about speakers it does make a difference as we’ll see later. The picture on the left shows a simple parallel circuit with the resistors again denoted by R1, R2, and R3; the voltage source shown by the epsilon symbol accompanied by the long and short parallel lines; and the nodes denoted by the red A and B. The picture at right shows the same circuit schematic written in a different manner. Note that these two circuits are equivalent it’s just easier to see the nodes in the first example.A note about the nodes, the voltage at node A must be the same for each resistor and similarly at node B. This means that the voltage across each resistor in a parallel circuit is the same.

Vt = VR1= VR2 = VR3

The current however is not provided with a single path to travel but multiple paths. This results in each resistor carrying part of the total current. The total current goes in at node A and splits between the resistors and “sums” back to the total at node B. Therefore the total current (I) in this parallel circuit is given as:

It = IR1 + IR2 + IR3

or:

It = ∑ IRi

The total resistance of this parallel circuit is a bit different. Instead of adding the value of each resistor together, we’re going to add the reciprocal of each value together and this gives us the reciprocal of the total resistance. I know that sounds weird but here’s what it looks like:

1/Rt = 1/R1 + 1/R2 + 1/R3

This can also be stated as:

Rt = 1/(1/R1 + 1/R2 + 1/R3)

Or:

Rt = 1/(∑ 1/Ri)

Using our example above of R1 = 8 ohms, R2 = 4 Ohms, and R3 = 2 ohms we have:

Rt = 1/(1/8 + 1/4 + 1/2)

Rt ≈1.1429Ω

Ohm’s Law states that:

V = IR

Or:

Voltage = Current x Resistance

Using this law one can find a missing value such as voltage when given the value of the current and resistance of the component. Using this in conjunction with Kirchhoff’s Laws, one can analyze an entire circuit. Keep in mind, we’re talking a circuit of just resistors, not including other electronic components such as capacitors, inductors, diodes, etc. This is just to give you a feel for the terms series and parallel.

You might be asking yourself “Okay, so now what?” and that’s ok. Let’s talk a bit about how this applies to your rig.

To you loyal readers who are with us every week, you know that last week I pulled a boo-boo and provided some incorrect information. I admitted it, corrected it, and spent my last day cleaning the bathroom today (it’s still pretty dirty, I’m no housekeeper). There were also some questions regarding series and parallel pickup configurations that I’ll try to clear up. This is not the main point of the article so it’s going to be brief.

When two pickups are in parallel, such as the 2 and 4 positions on a Strat, each provides a fairly low impedance inductive load on the other causing a filtering effect that produces that signature “quack” tone from a Strat.

When two pickups are wired in series, such as the

two coils in a humbucker, they do not load each other and the filtering effect is negligible and hardly even noticeable to most.

This information can be very useful. Ever wondered why people put a 4-way mod switch on a Tele? What’s up with that extra position? That would be a setting that puts both pickups in series providing a hotter output that is wonderful for lead playing as opposed to both pickups being in parallel like the standard middle position on a Tele. The use of a switch or the incredible S1 switch from Fender, will allow you to get this combination on your Strat as well as other wiring configurations that you wouldn’t normally think of. Now think about a humbucker. Last week we talked about coil-splitting for that single-coil tone. The bad thing about that is the split sound is just a single coil and subjected to noise. If you were to wire the switch to change the two coils to parallel operation instead of series, you would get a lower output tone that is similar to a single-coil but a bit fatter and you would still get the benefits of the hum-canceling.

We all have them and need them for our electric guitar glory but the whole cabinet impedance matching thing can be a bit confusing and tricky. Now that you have a little background on series and parallel, hopefully the “smoke and mirrors” behind impedance matching can be cleared up.

First of all, I have been asked many times what impedance is. Simple, impedance is resistance. First bit of smoke cleared up. Second, the same principles apply to series and parallel speaker wiring as to resistors in a circuit. A speaker acts as a large resistor with common values of 4Ω, 8Ω, and 16Ω. They can be wired both in series and in parallel or a combination of both to achieve the desired impedance. If all the speakers are the same impedance it’s easy to figure out the parallel and series impedance. If they’re in series, add ‘em up. Two 4 ohm speakers in series give you 8 ohms. Two 8 ohm speakers in series give you 16 ohms. When wiring speakers in parallel, if they are all the same impedance, the parallel impedance can be found by taking the impedance of one speaker and dividing it by the number of speakers that will be in parallel with it. For example, if you’re wiring two 16 ohm speakers in parallel, you will have a total load of 8 ohms. If you’re wiring 4 8 ohm speakers in parallel, you will have a total of 2 ohms. This is a really easy rule to remember if you don’t want to deal with the reciprocal equation shown above, however, in order for this to work, all the speakers __must be the same impedance.__ If you’re mixing and matching impedances, refer to the equation above to get your total impedance.

When you look at the back of a 2x12 cabinet and it says 8 ohms, this doesn’t mean it has two 8 ohm speakers in it, it means that the total impedance of the cabinet is 8 ohms. It more than likely has two 16 ohm speakers wired in parallel for a total of 8 ohms. When Marshall wires their stereo 4 x 12 (1960 series) cabinets they utilize two switching inputs as well as a DP/DT switch for switching between stereo and mono operation. When in stereo mode, each input is an 8 ohm input for either left or

right. When in mono mode the left input becomes a 16 ohm mono input and the right input becomes a 4 ohm mono input. The way this works is this; all the speakers are 16 ohm and are wired in a series/parallel combination meaning the two on the right are wired in a parallel pair (total impedance 8 ohms) and the two on the left are wired in a parallel pair (total impedance 8 ohms). The two pairs are then wired to switch between series/parallel depending on which jack you use. The right input switches the wiring between the pairs of speakers to parallel dropping the impedance to 4 ohms and the left input switches to the pairs being wired in series providing a 16 ohm input. The mono/stereo switch, splits the pairs in two providing a discreet input for each one.One last note before we go. When you are running two cabinets, you are almost always running the two cabinets in parallel. I cannot think of an amplifier that has multiple speaker outputs in series. That being said, always consult the documentation, just because I haven't seen it doesn't mean it doesn't exist. Also, if you’re using a single speaker output from your amplifier and daisy-chaining the cabinets together, those two cabinets are in parallel. The impedances of cabinets in parallel should be treated the same as speakers in parallel, in other words, two 8 ohm cabs in parallel result in a 4 ohm load and so on. Always remember to match the total impedance of your cabinets to the recommended output impedance of your tube amplifier or it could damage your amplifier. If you’re unsure, consult the manufacturer or a qualified technician.

Whew! That’s a lot of information packed into one article and I hope it didn’t make any heads explode. There are a lot of people out there who find this information fascinating and useful but it can get a bit confusing at times. I hope that this helps clear up a few things and provides a good reference for those wondering what the magic words “series” and “parallel” mean and how they apply to guitars in general. The speaker portion applies to any speaker cabinet, not just guitar cabinets. I hope you enjoyed the article. Thanks for reading folks, we’ll see you next time, in The Corner.

Source: proguitarshop.com

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