 Fundamentals

# Time to get series, and parallel, in perspective.

Bob Harper

Issue 10, April 2018

Time to get series, and parallel, in perspective.

We can talk about components until, well, forever, but components are useless without a good circuit. The principles of a circuit are fundamentally simple; deceptively simple, for some.

The Roman term “circuit” simply means a path that returns to the beginning, and you would be well advised to take that simple description very seriously. Most problems with circuits are caused by there not being a circuit at all.

I have had the experience of watching automotive mechanics making a group effort at curing an ignition issue on an old style car. Together they agreed on all of the important points in the circuit, inspected and tested them all, and concluded that everything was perfect. The engine had been out so I asked if the Earth Strap was in place. It wasn’t, so the spark circuit wasn’t earthed.

# PARTS OF A CIRCUIT

## The Path

The most important part of the circuit is the path; but the path isn’t just the conductors that connect the circuit, the path is how electrons get around the circuit, and make a complete circuit. Later, we will look at multiple path circuits, but for now, there must be at least one complete circuit.

If the only part of the circuit was the path, it would be a short circuit. Short circuits have no resistance or, in the real world, far less resistance than required for safety. A good image to help remember what a short circuit is, is to imagine a large spanner dropped across the terminals of a car battery. The alternative extreme is the open circuit. Open circuits have such high resistances that the circuit is effectively not connected. Most of the time that’s exactly what electricians mean by an open circuit, but at times there may be a small current flow caused by insulation leakage.

## Open and Closed Circuits

A part of the path is the control of the path, to either make the path “open” or “closed”. When you turn on the lights, you close the circuit allowing current to flow along the path to the lights. When you turn off the lights, you open the circuit, thus stopping the current.

Turning on or off is a term left over from old ceramic switches that had a knob to be turned left or right that turned the circuit on or off. Even the idea of opening and closing a circuit comes from a time when switches were a copper blade that was pushed into a socket to close the circuit, or pulled out to open the circuit. We called these “knife switches”.

## Insulation

The next most important part of a circuit is the insulation. Insulation prevents unintended connections between parts of the circuit, especially when the circuit is active (i.e., carrying current), which is also known as a “live” circuit.

To be effective, the insulation must separate the wires, and also hold them in place, and at the same time prevent the wires from contacting any conductive materials. The insulation provides protection to the wires from electrical potentials, mechanical damage, and chemical damage such as corrosion.

Every circuit needs a load, to prevent the circuit (path) becoming the load (i.e., the short circuit). The wiring has a very low resistance, hopefully less than one Ohm in many circuits. Therefore the load not only works for us, but it also protects the wiring from becoming a short circuit. The load is where the energy is converted into work, but as most people simply think it is “used up”, the load is sometimes also called the “sink”, essentially because the energy goes down the gurgler!

## Source

The final part of the circuit, although we could add a lot more details to all of the parts, is the source of energy, which is called the “source” by engineers and technicians. The source provides the electro-motive force, or “EMF”.

No doubt you are aware that the symbol “V” on a circuit refers to the voltage at that point; this also often means the potential difference (PD) between that point and ground, which should be the negative terminal of the source. Most of you will not have seen, or maybe not noticed the letter “E” at the source of a circuit, which is again referring to the EMF. So E or EMF refers to the source voltage, and V refers to the voltage at a point of a circuit, or between that point and the common or ground connection. E and V are both measured in volts.

Circuit = Source + Path + Sink

# SIMPLE CIRCUIT

The diagram below gives us the first type of electric circuit, but it is also the basis of pneumatic and hydraulic circuits, and many other systems.

A simple circuit has only one source, one path, and one load. Even if we connected the load directly across the battery terminals, there is still a path because the battery and the load, as conductors, are also a part of the path. Simple circuits are quite common; for example a hand held torch is a simple circuit, having a battery, a lamp, and the means of connecting it all. Importantly, the torch also has a switch, which although obvious, hasn’t been talked about much yet. The switch is a part of the path, in a group of components we call “control elements”. Most circuits have at least one control element such as a switch, fuse, relay or other means of stopping the circuit from draining the battery when not in use.

# SERIES CIRCUIT

The parts of a simple circuit are all connected in series, but the series circuit has more components than the simple circuit, having multiple loads, and sometimes multiple sources.

Our torch may have two or more cells connected in series, perhaps 3 x AA cells to form a 4.5V battery.

Note: a battery is actually a number of cells. The load may also have two or more load components connected in series; perhaps an LED and a resistor to limit the current in the LED, or simply a number of lamps - 3 x 1.5V lamps in this circuit, for example.

The important feature of a series circuit is that it only has one path.

All of the components in a series circuit are on the same path, but another term that we need to share is the term “node”. When a wire connects two components together, that wire is also a node. A node theoretically has no resistance between any points on that node, and in reality, a wire is considered a node as long as the resistance of the wire is so low it is insignificant to the circuit.

In a series circuit there is a node between every pair of components, but all of the nodes are along the same path. Therefore, the current in a series circuit passes through every component and node, meaning that the voltage across components, found by Ohm’s Law, must add up to the source voltage “E”, which is also called the “applied voltage”.

In engineering and science, the series circuit with it’s single path, has a single voltage loop, where all of the voltages - both the EMFs, and the voltage drops (Vd), or PD, across load components - all add together. Then, the sum of the EMFs must be equal to the sum of the PDs, and the total of all the voltages in the series circuit is zero.

# A SIDE ORDER OF VIRP

As an electrical teacher, there are always a few students finding electrical circuits, and the math involved, quite difficult. In an attempt to help students organise their work, and therefore their minds, I began using what I call “VIRP tables”, which is a method for circuit analysis that helps students organise their plan of attack.

VIRP stands for (V) voltage, (I) current, (R) resistance and (P) power.

As an explanatory comment, the symbol “I” doesn’t automatically cause you to think of “current” but if you go way, way back in electrical history, current was known as electric “intensity”, which left us using the letter “I” for current, as “C” was already used.

VIRP tables are intended to help students practise using Ohm’s law, and Kirchhoff’s Laws to calculate unknown values in a circuit, and to learn how, and when to apply each. VIRP can be habit forming however, so students should move on to more conventional methods, once the fundamentals are grasped. The VIRP method requires the student to draw a table with five headings that read: Part, V, I, R, P.

The student then labels the rows: E, R1, R2, R3, which represent each of the components in this circuit.

A row would exist for each component.

E refers to the source voltage, or EMF, and this row should be considered as the totals of V,I,R, and P.

The student then assesses what information the circuit diagram provides, and places the values in the table, taking care to write the values in the correct column and row, for the correct component. In our example table, we have written the known values in black.

V I R P
E 6V 160mA
R1 10Ω
R2 0.6W
R3

In any series circuit, the current is always the same, so any value of current in any part of a series circuit can be applied to every row including the current in the source (i.e., the total current). In our example table we have used pink to write the current in every row of the table under “I”.

V I R P
E 6V 160mA 37.5Ω 0.96W
R1 1.6V 160mA 10Ω 0.256W
R2 3.75V 160mA 23.43Ω 0.6W
R3 0.6512V 160mA 4.07Ω 0.104W

Now using Ohm’s law, or the power formula, for any component with two pieces of information, calculate the remaining two values, and add them to the table.

In row E we used Ohm's Law and the Power Rule to calculate the total resistance and the total power, and added the values in grey.

In row R1 we calculated the voltage and the power.

In row R2 we calculated the voltage and the resistance.

Note how easy it is to see what you know, and what you need to find or calculate; just like filling in a crossword puzzle! The remaining tool available to the student is for Kirchhoff’s Voltage Law (“KVL” used in a series circuit). This states: “The sum of the applied EMFs is equal to the sum of the voltage drops”, and is used to calculate the remaining voltage value.

Two more useful pieces of information about a series circuit are:

1. The total resistance is the sum of all the individual resistances; and;

2. The total power used in the circuit is equal to the sum of the power used in all the components.

The VIRP wheel is a good way to remember the variations of Ohm’s Law and the power rule. The two formulae are transposed so those with difficulty understanding transposition can, regrettably but by their own choice, learn by ROTE. It is far better to learn V=IR and P=VI, and learn to transpose, but this little helper can get people past the barrier, allowing them to gradually learn how transposition works. # PARALLEL CIRCUIT

The problem with series circuits is that the applied voltage must be the sum of the voltage drops. While this is okay for Christmas tree lights (unless one is blown), it’s no good in a house or industry, or for electric power distribution. For example, when you buy a 230V toaster, you expect to plug it into a 230V socket and have it work. Power distribution is all parallel circuits, but the loads may include series circuits, as well as others we haven’t discussed yet. The important feature of a parallel circuit is that it only has two Nodes.

The loads on a parallel circuit are not only connected in parallel to each other, but in parallel with the source. This means that there are only two nodes: one is the same as the negative of the battery, and is usually known as the ground in DC circuits, also sometimes labelled as “negative”, “-ve” or “V-". The other node is connected to the positive terminal of the battery, and is labelled as “positive”, “+ve” or “V+”.

All of the components in a parallel circuit are connected between these two nodes, and they might, for illustration purposes, be soldered to two copper sheets.

The wiring of the path consists of two nodes, regardless of how the wires join the components, or how many wires are used.

The power switch may at first cause some argument, but when the circuit is operating, the switch is zero resistance, theoretically and hopefully so.

Although switches in circuits are usually shown in the open circuit position, when the switch is closed and current flows, the switch is a part of the node and the connections either side are considered as the same node.

If the voltage is always the same across every component in a parallel circuit, then the current in the components will be determined by Ohm’s Law, and according to Kirchhoff's Current Law (KCL) the current in the components will add up to the current provided by the source (i.e., the sum of the source currents is equal to the sum of the load currents.

VIRP tables can also make parallel circuit calculations easy, remembering that in parallel circuits, the voltage is always the same, not the current.

Try this one yourself:

In a parallel circuit the voltage is 12VDC, R1 = 12Ω, R2 takes 0.5A, and R3 uses 1.2W of power. That’s your homework! Hint: Draw the circuit, draw the VIRP table, Write the values on both the circuit and the VIRP table, and think it through!

# COMPOUND CIRCUIT

No doubt, this is where electrical students either show their mettle or lose interest in what we call “circuit analysis”.

Compound circuits combine both series circuits and parallel circuit elements, so compound circuits always have more than one path and more than two nodes. They also follow all of the rules of series circuits, for the series parts, and parallel circuits for the parallel parts, which makes compound circuits a little like crossword puzzles; you look at what you know, and look for something that you can learn using Ohm’s Law, and what you know about series, and parallel circuits, or at least components wired in series or parallel. The important feature of a compound circuit is that it has more than one path and more than two Nodes.

Compound circuits are more common than you might think and almost every appliance in the home is typically a compound circuit. Your house is basically a parallel circuit, but the things you plug in may be series, parallel, or compound circuits. Alternatively, they may be the most difficult of circuits, the complex circuit.

# COMPLEX CIRCUIT

Complex circuits are, indeed, more complex! I suppose we could say that any circuit that does not easily fit into any of the first four circuit types, is most likely a complex circuit. Typically, complex circuits have current from one parallel leg being diverted into another parallel leg, or two energy sources feeding a common load through other load elements. Generally speaking, electricians only need to learn the first four types, but it pays to be aware of complex circuits; you just want to hope they are left for the engineers and scientists to sort out (as we’ll do in this article, at least for now!).

The important feature of a complex circuit is that components cannot be clearly sorted into series and parallel elements.

# THE CUBE PROBLEM

Chances are, now you know that complex circuits exist, you want to learn why they are called “complex”.

Assume that a cube shape is made out of 12 resistors of the same resistance (e.g., 12 @ 1000 Ohm resistors). The resistors represent the edges of a cube, which is made by soldering three resistors together at each corner (i.e., node). The result is a cube with 12 edges, 8 nodes and 6 faces.

Note: As an electrical circuit, no matter which two nodes you choose to connect to the battery, the cube will have three paths. Check it for yourself.

Now, calculate the total resistance of the cube, as measured across opposite corners of the space, (i.e., diametrically opposite corners on a line passing through the centre of the cube).

You don’t have to make it, but this is the cheat’s way to find the value we are looking for, using a plastic multimeter instead of the brain (the multimeter should give a value of 833 Ohms, but the more important question is “why?”).

Note: The internet has this problem on many sites, and there are several accepted methods for solving the same problem.  # FINAL THOUGHTS

To keep this to one article, rather than three or more chapters of a textbook, I have left out concepts that my TAFE Electrical Teacher friends love: Kirchhoff’s Voltage and Current Laws, Node and Loop analysis, and more. But, we must leave some things for another day!

# VIRP Challenge

See if you can fill in the blanks without referencing the original! DIYODE Magazine readers range from “newbies” to university lecturers, and everywhere in between; but when I was teaching, the VIRP Wheel was not allowed in class (although some colleges “accidentally” left a copy on the wall of the first year classrooms).

Of course, it is far better to avoid relying on such resources, as they won’t always be available for you to refer to. Therefore, my students were often challenged to take a blank sheet of paper and to draw and fill in the VIRP Wheel for themselves. This is an exercise in both memory and transposition, which requires you to think past attempting to remember the formulae, and actually learn the principles that the formulae refers to.

For many years, governments have chosen to call TAFE (Technical and Further Education) a training institution, and some training is involved in some courses, but TAFE is an Educational Institution, teaching our tradespeople and others how to think.

Remembering formulae is a very difficult task, but if you don’t understand principles, and instead merely complete jobs by ROTE learning, the result is a loss of education.

Think of the brain as a learning muscle: to make it strong, you need to give it plenty of exercise!