Resistors determine the flow of current in an electrical circuit. Where there is high resistance in a circuit the flow of current is small, where the resistance is low the flow of current is large. Resistance, voltage and current are connected in an electrical circuit by Ohm’s Law

   When a resistor is introduced to a circuit the flow of current is reduced. The higher the value of the resistor the smaller/lower the flow of current.

   Resistors are used for regulating current and they resist the current flow and the extent to which they do this is measured in ohms (Ω). Resistors are found in almost every electronic circuit.

   The most common type of resistor consists of a small ceramic (clay) tube covered partially by a conducting carbon film. The composition of the carbon determines how much current can pass through.

   Resistors can be connected together in two ways to give different overall values. This is especially useful if you do not have a resistor of the correct value and need to make it up from other available ones.

 1. Resistors in SERIES - When resistors are connected in series, their values are added together:

 R total=R1+R2

 2. Resistors in PARALLEL -When resistors are connected in parallel, their total resistance is given as:

 1/Rtotal = 1/R1 + 1/R2


   Variable resistors have adjustable values. Adjustment is normally made by turning a spindle (e.g. the volume control on a radio) or moving a slider.

   The rotary variable resistor is the cheapest type of variable resistor. A smaller version of this variable resistor is the pre-set resistor. The pre-set resistor is the type usually used in small electronic projects


   Capacitors store electric charge. They are used with resistors in timing circuits because it takes time for a capacitor to fill with charge. They are used to smooth varying DC supplies by acting as a reservoir of charge. They are also used in filter circuits because capacitors easily pass AC (changing) signals but they block DC (constant) signals.


   This is a measure of a capacitor's ability to store charge. A large capacitance means that more charge can be stored. Capacitance is measured in farads, symbol F. However 1F is very large, so prefixes are used to show the smaller values.

   Three prefixes (multipliers) are used, µ (micro), n (nano) and p (pico):

  • µ means 10-6 (millionth), so 1000000µF = 1F
  • n means 10-9 (thousand-millionth), so 1000nF = 1µF
  • p means 10-12 (million-millionth), so 1000pF = 1nF

   Capacitor values can be very difficult to find because there are many types of capacitor with different labelling systems!


   Electrolytic capacitors are polarised and they must be connected the correct way round, at least one of their leads will be marked + or -. They are not damaged by heat when soldering.

   There are two designs of electrolytic capacitors; axial where the leads are attached to each end (220µF in picture) and radial where both leads are at the same end (10µF in picture). Radial capacitors tend to be a little smaller and they stand upright on the circuit board.

   It is easy to find the value of electrolytic capacitors because they are clearly printed with their capacitance and voltage rating. The voltage rating can be quite low (6V for example) and it should always be checked when selecting an electrolytic capacitor. If the project parts list does not specify a voltage, choose a capacitor with a rating which is greater than the project's power supply voltage. 25V is a sensible minimum for most battery circuits.

 Tantalum Bead Capacitors

   Tantalum bead capacitors are polarised and have low voltage ratings like electrolytic capacitors. They are expensive but very small, so they are used where a large capacitance is needed in a small size.

   Modern tantalum bead capacitors are printed with their capacitance, voltage and polarity in full. However older ones use a colour-code system which has two stripes (for the two digits) and a spot of colour for the number of zeros to give the value in µF. The standard colour code is used, but for the spot, grey is used to mean × 0.01 and white means × 0.1 so that values of less than 10µF can be shown. A third colour stripe near the leads shows the voltage (yellow 6.3V, black 10V, green 16V, blue 20V, grey 25V, white 30V, pink 35V). The positive (+) lead is to the right when the spot is facing you: 'when the spot is in sight, the positive is to the right'. tantalum bead capacitors

For example: blue, grey, black spot means 68µF
For example: blue, grey, white spot means 6.8µF
For example: blue, grey, grey spot means 0.68µF


Unpolarised capacitors (small values, up to 1µF)


   Small value capacitors are unpolarised and may be connected either way round. They are not damaged by heat when soldering, except for one unusual type (polystyrene). They have high voltage ratings of at least 50V, usually 250V or so. It can be difficult to find the values of these small capacitors because there are many types of them and several different labelling systems!

100nF capacitor    Many small value capacitors have their value printed but without a multiplier, so you need to use experience to work out what the multiplier should be!

For example 0.1 means 0.1µF = 100nF.

   Sometimes the multiplier is used in place of the decimal point:
For example: 4n7 means 4.7nF.

Capacitor Number Code

A number code is often used on small capacitors where printing is difficult: 1nF capacitor

  • the 1st number is the 1st digit,
  • the 2nd number is the 2nd digit,
  • the 3rd number is the number of zeros to give the capacitance in pF.
  • Ignore any letters - they just indicate tolerance and voltage rating.

For example: 102 means 1000pF = 1nF (not 102pF!)

For example: 472J means 4700pF = 4.7nF (J means 5% tolerance).

Colour Code
Colour Number

Capacitor Colour Code

   A colour code was used on polyester capacitors for many years. It is now obsolete, but of course there are many still around. The colours should be read like the resistor code, the top three colour bands giving the value in pF. Ignore the 4th band (tolerance) and 5th band (voltage rating). 10nF and 220nF capacitors

For example:

brown, black, orange means 10000pF = 10nF = 0.01µF.

   Note that there are no gaps between the colour bands, so 2 identical bands actually appear as a wide band.

For example:

wide red, yellow means 220nF = 0.22µF.

Polystyrene Capacitors

polystyrene capacitor    This type is rarely used now. Their value (in pF) is normally printed without units. Polystyrene capacitors can be damaged by heat when soldering (it melts the polystyrene!) so you should use a heat sink (such as a crocodile clip). Clip the heat sink to the lead between the capacitor and the joint.

Real capacitor values (the E3 and E6 series)

You may have noticed that capacitors are not available with every possible value, for example 22µF and 47µF are readily available, but 25µF and 50µF are not!

Why is this? Imagine that you decided to make capacitors every 10µF giving 10, 20, 30, 40, 50 and so on. That seems fine, but what happens when you reach 1000? It would be pointless to make 1000, 1010, 1020, 1030 and so on because for these values 10 is a very small difference, too small to be noticeable in most circuits and capacitors cannot be made with that accuracy.

To produce a sensible range of capacitor values you need to increase the size of the 'step' as the value increases. The standard capacitor values are based on this idea and they form a series which follows the same pattern for every multiple of ten.

The E3 series (3 values for each multiple of ten)
10, 22, 47, ... then it continues 100, 220, 470, 1000, 2200, 4700, 10000 etc.
Notice how the step size increases as the value increases (values roughly double each time).

The E6 series (6 values for each multiple of ten)
10, 15, 22, 33, 47, 68, ... then it continues 100, 150, 220, 330, 470, 680, 1000 etc.
Notice how this is the E3 series with an extra value in the gaps.

The E3 series is the one most frequently used for capacitors because many types cannot be made with very accurate values.


Variable capacitors

variable capacitor
Variable Capacitor
Photograph © Rapid Electronics
Variable capacitors are mostly used in radio tuning circuits and they are sometimes called 'tuning capacitors'. They have very small capacitance values, typically between 100pF and 500pF (100pF = 0.0001µF). The type illustrated usually has trimmers built in (for making small adjustments - see below) as well as the main variable capacitor.

Many variable capacitors have very short spindles which are not suitable for the standard knobs used for variable resistors and rotary switches. It would be wise to check that a suitable knob is available before ordering a variable capacitor.

Variable capacitors are not normally used in timing circuits because their capacitance is too small to be practical and the range of values available is very limited. Instead timing circuits use a fixed capacitor and a variable resistor if it is necessary to vary the time period.


Trimmer capacitors

trimmer capacitor
Trimmer Capacitor
Photograph © Rapid Electronics
Trimmer capacitors (trimmers) are miniature variable capacitors. They are designed to be mounted directly onto the circuit board and adjusted only when the circuit is built.

A small screwdriver or similar tool is required to adjust trimmers. The process of adjusting them requires patience because the presence of your hand and the tool will slightly change the capacitance of the circuit in the region of the trimmer!

Trimmer capacitors are only available with very small capacitances, normally less than 100pF. It is impossible to reduce their capacitance to zero, so they are usually specified by their minimum and maximum values, for example 2-10pF.

Trimmers are the capacitor equivalent of presets which are miniature variable resistors.

 Induction and Inductance



In 1824, Oersted discovered that current passing though a coil created a magnetic field capable of shifting a compass needle. Seven years later, Faraday and Henry discovered just the opposite. They noticed that a moving magnetic field would induce current in an electrical conductor. This process of generating electrical current in a conductor by placing the conductor in a changing magnetic field is called electromagnetic induction or just induction. It is called induction because the current is said to be induced in the conductor by the magnetic field.

Faraday also noticed that the rate at which the magnetic field changed also had an effect on the amount of current or voltage that was induced. Faraday's Law for an uncoiled conductor states that the amount of induced voltage is proportional to the rate of change of flux lines cutting the conductor. Faraday's Law for a straight wire is shown below.


VL = the induced voltage in volts
dø/dt = the rate of change of magnetic flux in webers/second

Induction is measured in unit of Henries (H) which reflects this dependence on the rate of change of the magnetic field. One henry is the amount of inductance that is required to generate one volt of induced voltage when the current is changing at the rate of one ampere per second. Note that current is used in the definition rather than magnetic field. This is because current can be used to generate the magnetic field and is easier to measure and control than magnetic flux.


When induction occurs in an electrical circuit and affects the flow of electricity it is called inductance, L. Self-inductance, or simply inductance, is the property of a circuit whereby a change in current causes a change in voltage in the same circuit. When one circuit induces current flow in a second nearby circuit, it is known as mutual-inductance. The image to the right shows an example of mutual-inductance. When an AC current is flowing through a piece of wire in a circuit, an electromagnetic field is produced that is constantly growing and shrinking and changing direction due to the constantly changing current in the wire. This changing magnetic field will induce electrical current in another wire or circuit that is brought close to the wire in the primary circuit. The current in the second wire will also be AC and in fact will look very similar to the current flowing in the first wire. An electrical transformer uses inductance to change the voltage of electricity into a more useful level. In nondestructive testing, inductance is used to generate eddy currents in the test piece.

It should be noted that since it is the changing magnetic field that is responsible for inductance, it is only present in AC circuits. High frequency AC will result in greater inductive reactance since the magnetic field is changing more rapidly.

Self-inductance and mutual-inductance will be discussed in more detail in the following pages.


Self-Inductance and Inductive Reactance

The property of self-inductance is a particular form of electromagnetic induction. Self inductance is defined as the induction of a voltage in a current-carrying wire when the current in the wire itself is changing. In the case of self-inductance, the magnetic field created by a changing current in the circuit itself induces a voltage in the same circuit. Therefore, the voltage is self-induced.

The term inductor is used to describe a circuit element possessing the property of inductance and a coil of wire is a very common inductor. In circuit diagrams, a coil or wire is usually used to indicate an inductive component. Taking a closer look at a coil will help understand the reason that a voltage is induced in a wire carrying a changing current. The alternating current running through the coil creates a magnetic field in and around the coil that is increasing and decreasing as the current changes. The magnetic field forms concentric loops that surround the wire and join to form larger loops that surround the coil as shown in the image below. When the current increases in one loop the expanding magnetic field will cut across some or all of the neighboring loops of wire, inducing a voltage in these loops. This causes a voltage to be induced in the coil when the current is changing.

By studying this image of a coil, it can be seen that the number of turns in the coil will have an effect on the amount of voltage that is induced into the circuit. Increasing the number of turns or the rate of change of magnetic flux increases the amount of induced voltage. Therefore, Faraday's Law must be modified for a coil of wire and becomes the following.


VL = induced voltage in volts
N = number of turns in the coil
dø/dt = rate of change of magnetic flux in

The equation simply states that the amount of induced voltage (VL) is proportional to the number of turns in the coil and the rate of change of the magnetic flux (dø/dt). In other words, when the frequency of the flux is increased or the number of turns in the coil is increased, the amount of induced voltage will also increase.

In a circuit, it is much easier to measure current than it is to measure magnetic flux, so the following equation can be used to determine the induced voltage if the inductance and frequency of the current are known. This equation can also be reorganized to allow the inductance to be calculated when the amount of inducted voltage can be determined and the current frequency is known.


VL = the induced voltage in volts
L = the value of inductance in henries
di/dt = the rate of change of current in amperes per second

Lenz's Law

Soon after Faraday proposed his law of induction, Heinrich Lenz developed a rule for determining the direction of the induced current in a loop. Basically, Lenz's law states that an induced current has a direction such that its magnetic field opposes the change in magnetic field that induced the current. This means that the current induced in a conductor will oppose the change in current that is causing the flux to change. Lenz's law is important in understanding the property of inductive reactance, which is one of the properties measured in eddy current testing.

Inductive Reactance

The reduction of current flow in a circuit due to induction is called inductive reactance. By taking a closer look at a coil of wire and applying Lenz's law, it can be seen how inductance reduces the flow of current in the circuit. In the image below, the direction of the primary current is shown in red, and the magnetic field generated by the current is shown in blue. The direction of the magnetic field can be determined by taking your right hand and pointing your thumb in the direction of the current. Your fingers will then point in the direction of the magnetic field. It can be seen that the magnetic field from one loop of the wire will cut across the other loops in the coil and this will induce current flow (shown in green) in the circuit. According to Lenz's law, the induced current must flow in the opposite direction of the primary current. The induced current working against the primary current results in a reduction of current flow in the circuit.

It should be noted that the inductive reactance will increase if the number of winds in the coil is increased since the magnetic field from one coil will have more coils to interact with.

Similarly to resistance, inductive reactance reduces the flow of current in a circuit. However, it is possible to distinguish between resistance and inductive reactance in a circuit by looking at the timing between the sine waves of the voltage and current of the alternating current. In an AC circuit that contains only resistive components, the voltage and the current will be in-phase, meaning that the peaks and valleys of their sine waves will occur at the same time. When there is inductive reactance present in the circuit, the phase of the current will be shifted so that its peaks and valleys do not occur at the same time as those of the voltage. This will be discussed in more detail in the section on circuits.


Mutual Inductance
(The Basis for Eddy Current Inspection)

The magnetic flux through a circuit can be related to the current in that circuit and the currents in other nearby circuits, assuming that there are no nearby permanent magnets. Consider the following two circuits.

The magnetic field produced by circuit 1 will intersect the wire in circuit 2 and create current flow. The induced current flow in circuit 2 will have its own magnetic field which will interact with the magnetic field of circuit 1. At some point P, the magnetic field consists of a part due to i1 and a part due to i2. These fields are proportional to the currents producing them.

The coils in the circuits are labeled L1 and L2 and this term represents the self inductance of each of the coils. The values of L1 and L2 depend on the geometrical arrangement of the circuit (i.e. number of turns in the coil) and the conductivity of the material. The constant M, called the mutual inductance of the two circuits, is dependent on the geometrical arrangement of both circuits. In particular, if the circuits are far apart, the magnetic flux through circuit 2 due to the current i1 will be small and the mutual inductance will be small. L2 and M are constants.

We can write the flux, B through circuit 2 as the sum of two parts.

B2 = L2i2 + i1M

An equation similar to the one above can be written for the flux through circuit 1.

B1 = L1i1 + i2M

Though it is certainly not obvious, it can be shown that the mutual inductance is the same for both circuits. Therefore, it can be written as follows:

M1,2 = M2,1

How is mutual induction used in eddy current inspection?

In eddy current inspection, the eddy currents are generated in the test material due to mutual induction. The test probe is basically a coil of wire through which alternating current is passed. Therefore, when the probe is connected to an eddyscope instrument, it is basically represented by circuit 1 above. The second circuit can be any piece of conductive material.

When alternating current is passed through the coil, a magnetic field is generated in and around the coil. When the probe is brought in close proximity to a conductive material, such as aluminum, the probe's changing magnetic field generates current flow in the material. The induced current flows in closed loops in planes perpendicular to the magnetic flux. They are named eddy currents because they are thought to resemble the eddy currents that can be seen swirling in streams.

The eddy currents produce their own magnetic fields that interact with the primary magnetic field of the coil. By measuring changes in the resistance and inductive reactance of the coil, information can be gathered about the test material. This information includes the electrical conductivity and magnetic permeability of the material, the amount of material cutting through the coils magnetic field, and the condition of the material (i.e. whether it contains cracks or other defects.) The distance that the coil is from the conductive material is called liftoff, and this distance affects the mutual-inductance of the circuits. Liftoff can be used to make measurements of the thickness of nonconductive coatings, such as paint, that hold the probe a certain distance from the surface of the conductive material.

It should be noted that if a sample is ferromagnetic, the magnetic flux is concentrated and strengthened despite opposing eddy current effects. The increase inductive reactance due to the magnetic permeability of ferromagnetic materials makes it easy to distinguish these materials from nonferromagnetic materials.

In the applet below, the probe and the sample are shown in cross-section. The boxes represent the cross-sectional area of a group of turns in the coil. The liftoff distance and the drive current of the probe can be varied to see the effects of the shared magnetic field. The liftoff value can be set to 0.1 or less and the current value can be varied from 0.01 to 1.0. The strength of the magnetic field is shown by the darkness of the lines.