Component failure analysis

The job of a technician frequently entails “troubleshooting” (locating and correcting a problem) in malfunctioning circuits. Good troubleshooting is a demanding and rewarding effort, requiring a thorough understanding of the basic concepts, the ability to formulate hypotheses (proposed explanations of an effect), the ability to judge the value of different hypotheses based on their probability (how likely one particular cause may be over another), and a sense of creativity in applying a solution to rectify the problem. While it is possible to distill these skills into a scientific methodology, most practiced troubleshooters would agree that troubleshooting involves a touch of art, and that it can take years of experience to fully develop this art.
An essential skill to have is a ready and intuitive understanding of how component faults affect circuits in different configurations. We will explore some of the effects of component faults in both series and parallel circuits here, then to a greater degree at the end of the “Series-Parallel Combination Circuits” chapter.
Let’s start with a simple series circuit:

With all components in this circuit functioning at their proper values, we can mathematically determine all currents and voltage drops:

Now let us suppose that R2 fails shorted. Shorted means that the resistor now acts like a straight piece of wire, with little or no resistance. The circuit will behave as though a “jumper” wire were connected across R2 (in case you were wondering, “jumper wire” is a common term for a temporary wire connection in a circuit). What causes the shorted condition of R2 is no matter to us in this example; we only care about its effect upon the circuit:

With R2 shorted, either by a jumper wire or by a internal resistor failure, the total circuit resistance will decrease. Since the voltage output by the battery is a constant (at least in our ideal simulation here), a decrease in total circuit resistance means that total circuit current must increase:

As the circuit current increases from 20 milliamps to 60 milliamps, the voltage drops across R1 and R3 (which haven’t changed resistances) increase as well, so that the two resistors are dropping the whole 9 volts. R2, being bypassed by the very low resistance of the jumper wire, is effectively eliminated from the circuit, the resistance from one lead to the other having been reduced to zero. Thus, the voltage drop across R2, even with the increased total current, is zero volts.
On the other hand, if R2 were to fail “open” — resistance increasing to nearly infinite levels — it would also create wide-reaching effects in the rest of the circuit:

With R2 at infinite resistance and total resistance being the sum of all individual resistances in a series circuit, the total current decreases to zero. With zero circuit current, there is no electron flow to produce voltage drops across R1 or R3. R2, on the other hand, will manifest the full supply voltage across its terminals.
We can apply the same before/after analysis technique to parallel circuits as well. First, we determine what a “healthy” parallel circuit should behave like.

Supposing that R2 opens in this parallel circuit, here’s what the effects will be:

Notice that in this parallel circuit, an open branch only affects the current through that branch and the circuit’s total current. Total voltage — being shared equally across all components in a parallel circuit, will be the same for all resistors. Due to the fact that the voltage source’s tendency is to hold voltage constant, its voltage will not change, and being in parallel with all the resistors, it will hold all the resistors’ voltages the same as they were before: 9 volts. Being that voltage is the only common parameter in a parallel circuit, and the other resistors haven’t changed resistance value, their respective branch currents remain unchanged.
This is what happens in a household lamp circuit: all lamps get their operating voltage from power wiring arranged in a parallel fashion. Turning one lamp on and off (one branch in that parallel circuit closing and opening) doesn’t affect the operation of other lamps in the room, only the current in that one lamp (branch circuit) and the total current powering all the lamps in the room:

In an ideal case (with perfect voltage sources and zero-resistance connecting wire), shorted resistors in a simple parallel circuit will also have no effect on what’s happening in other branches of the circuit. In real life, the effect is not quite the same, and we’ll see why in the following example:

A shorted resistor (resistance of 0 Ω) would theoretically draw infinite current from any finite source of voltage (I=E/0). In this case, the zero resistance of R2 decreases the circuit total resistance to zero Ω as well, increasing total current to a value of infinity. As long as the voltage source holds steady at 9 volts, however, the other branch currents (IR1 and IR3) will remain unchanged.
The critical assumption in this “perfect” scheme, however, is that the voltage supply will hold steady at its rated voltage while supplying an infiniteamount of current to a short-circuit load. This is simply not realistic. Even if the short has a small amount of resistance (as opposed to absolutely zero resistance), no real voltage source could arbitrarily supply a huge overload current and maintain steady voltage at the same time. This is primarily due to the internal resistance intrinsic to all electrical power sources, stemming from the inescapable physical properties of the materials they’re constructed of:

These internal resistances, small as they may be, turn our simple parallel circuit into a series-parallel combination circuit. Usually, the internal resistances of voltage sources are low enough that they can be safely ignored, but when high currents resulting from shorted components are encountered, their effects become very noticeable. In this case, a shorted R2 would result in almost all the voltage being dropped across the internal resistance of the battery, with almost no voltage left over for resistors R1, R2, and R3:

Suffice it to say, intentional direct short-circuits across the terminals of any voltage source is a bad idea. Even if the resulting high current (heat, flashes, sparks) causes no harm to people nearby, the voltage source will likely sustain damage, unless it has been specifically designed to handle short-circuits, which most voltage sources are not.
Eventually in this book I will lead you through the analysis of circuits without the use of any numbers, that is, analyzing the effects of component failure in a circuit without knowing exactly how many volts the battery produces, how many ohms of resistance is in each resistor, etc. This section serves as an introductory step to that kind of analysis.
Whereas the normal application of Ohm’s Law and the rules of series and parallel circuits is performed with numerical quantities (“quantitative”), this new kind of analysis without precise numerical figures is something I like to call qualitative analysis. In other words, we will be analyzing the qualities of the effects in a circuit rather than the precise quantities. The result, for you, will be a much deeper intuitive understanding of electric circuit operation.

Building simple resistor circuits

In the course of learning about electricity, you will want to construct your own circuits using resistors and batteries. Some options are available in this matter of circuit assembly, some easier than others. In this section, I will explore a couple of fabrication techniques that will not only help you build the circuits shown in this chapter, but also more advanced circuits.
If all we wish to construct is a simple single-battery, single-resistor circuit, we may easily use alligator clip jumper wires like this:

Jumper wires with “alligator” style spring clips at ach end provide a safe and convenient method of electrically joining components together.
If we wanted to build a simple series circuit with one battery and three resistors, the same “point-to-point” construction technique using jumper wires could be applied:

This technique, however, proves impractical for circuits much more complex than this, due to the awkwardness of the jumper wires and the physical fragility of their connections. A more common method of temporary construction for the hobbyist is the solderless breadboard, a device made of plastic with hundreds of spring-loaded connection sockets joining the inserted ends of components and/or 22-gauge solid wire pieces. A photograph of a real breadboard is shown here, followed by an illustration showing a simple series circuit constructed on one:
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Underneath each hole in the breadboard face is a metal spring clip, designed to grasp any inserted wire or component lead. These metal spring clips are joined underneath the breadboard face, making connections between inserted leads. The connection pattern joins every five holes along a vertical column (as shown with the long axis of the breadboard situated horizontally):

Thus, when a wire or component lead is inserted into a hole on the breadboard, there are four more holes in that column providing potential connection points to other wires and/or component leads. The result is an extremely flexible platform for constructing temporary circuits. For example, the three-resistor circuit just shown could also be built on a breadboard like this:

A parallel circuit is also easy to construct on a solderless breadboard:

Breadboards have their limitations, though. First and foremost, they are intended for temporary construction only. If you pick up a breadboard, turn it upside-down, and shake it, any components plugged into it are sure to loosen, and may fall out of their respective holes. Also, breadboards are limited to fairly low-current (less than 1 amp) circuits. Those spring clips have a small contact area, and thus cannot support high currents without excessive heating.
For greater permanence, one might wish to choose soldering or wire-wrapping. These techniques involve fastening the components and wires to some structure providing a secure mechanical location (such as a phenolic or fiberglass board with holes drilled in it, much like a breadboard without the intrinsic spring-clip connections), and then attaching wires to the secured component leads. Soldering is a form of low-temperature welding, using a tin/lead or tin/silver alloy that melts to and electrically bonds copper objects. Wire ends soldered to component leads or to small, copper ring “pads” bonded on the surface of the circuit board serve to connect the components together. In wire wrapping, a small-gauge wire is tightly wrapped around component leads rather than soldered to leads or copper pads, the tension of the wrapped wire providing a sound mechanical and electrical junction to connect components together.
An example of a printed circuit board, or PCB, intended for hobbyist use is shown in this photograph:
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This board appears copper-side-up: the side where all the soldering is done. Each hole is ringed with a small layer of copper metal for bonding to the solder. All holes are independent of each other on this particular board, unlike the holes on a solderless breadboard which are connected together in groups of five. Printed circuit boards with the same 5-hole connection pattern as breadboards can be purchased and used for hobby circuit construction, though.
Production printed circuit boards hav traces of copper laid down on the phenolic or fiberglass substrate material to form pre-engineered connection pathways which function as wires in a circuit. An example of such a board is shown here, this unit actually a “power supply” circuit designed to take 120 volt alternating current (AC) power from a household wall socket and transform it into low-voltage direct current (DC). A resistor appears on this board, the fifth component counting up from the bottom, located in the middle-right area of the board.
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A view of this board’s underside reveals the copper “traces” connecting components together, as well as the silver-colored deposits of solder bonding the component leads to those traces:
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A soldered or wire-wrapped circuit is considered permanent: that is, it is unlikely to fall apart accidently. However, these construction techniques are sometimes considered too permanent. If anyone wishes to replace a component or change the circuit in any substantial way, they must invest a fair amount of time undoing the connections. Also, both soldering and wire-wrapping require specialized tools which may not be immediately available.
An alternative construction technique used throughout the industrial world is that of the terminal strip. Terminal strips, alternatively called barrier strips or terminal blocks, are comprised of a length of nonconducting material with several small bars of metal embedded within. Each metal bar has at least one machine screw or other fastener under which a wire or component lead may be secured. Multiple wires fastened by one screw are made electrically common to each other, as are wires fastened to multiple screws on the same bar. The following photograph shows one style of terminal strip, with a few wires attached.
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Another, smaller terminal strip is shown in this next photograph. This type, sometimes referred to as a “European” style, has recessed screws to help prevent accidental shorting between terminals by a screwdriver or other metal object:
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In the following illustration, a single-battery, three-resistor circuit is shown constructed on a terminal strip:

If the terminal strip uses machine screws to hold the component and wire ends, nothing but a screwdriver is needed to secure new connections or break old connections. Some terminal strips use spring-loaded clips — similar to a breadboard’s except for increased ruggedness — engaged and disengaged using a screwdriver as a push tool (no twisting involved). The electrical connections established by a terminal strip are quite robust, and are considered suitable for both permanent and temporary construction.
One of the essential skills for anyone interested in electricity and electronics is to be able to “translate” a schematic diagram to a real circuit layout where the components may not be oriented the same way. Schematic diagrams are usually drawn for maximum readability (excepting those few noteworthy examples sketched to create maximum confusion!), but practical circuit construction often demands a different component orientation. Building simple circuits on terminal strips is one way to develop the spatial-reasoning skill of “stretching” wires to make the same connection paths. Consider the case of a single-battery, three-resistor parallel circuit constructed on a terminal strip:

Progressing from a nice, neat, schematic diagram to the real circuit — especially when the resistors to be connected are physically arranged in a linear fashion on the terminal strip — is not obvious to many, so I’ll outline the process step-by-step. First, start with the clean schematic diagram and all comonents secured to the terminal strip, with no connecting wires:

Next, trace the wire connection from one side of the battery to the first component in the schematic, securing a connecting wire between the same two points on the real circuit. I find it helpful to over-draw the schematic’s wire with another line to indicate what connections I’ve made in real life:

Continue this process, wire by wire, until all connections in the schematic diagram have been accounted for. It might be helpful to regard common wires in a SPICE-like fashion: make all connections to a common wire in the circuit as one step, making sure each and every component with a connection to that wire actually has a connection to that wire before proceeding to the next. For the next step, I’ll show how the top sides of the remaining two resistors are connected together, being common with the wire secured in the previous step:

With the top sides of all resistors (as shown in the schematic) connected together, and to the battery’s positive (+) terminal, all we have to do now is connect the bottom sides together and to the other side of the battery:

Typically in industry, all wires are labeled with number tags, and electrically common wires bear the same tag number, just as they do in a SPICE simulation. In this case, we could label the wires 1 and 2:

Another industrial convention is to modify the schematic diagram slightly so as to indicate actual wire connection points on the terminal strip. This demands a labeling system for the strip itself: a “TB” number (terminal block number) for the strip, followed by another number representing each metal bar on the strip.

This way, the schematic may be used as a “map” to locate points in a real circuit, regardless of how tangled and complex the connecting wiring may appear to the eyes. This may seem excessive for the simple, three-resistor circuit shown here, but such detail is absolutely necessary for construction and maintenance of large circuits, especially when those circuits may span a great physical distance, using more than one terminal strip located in more than one panel or box.