Musical Controllers Workshop

Sonology B2

The MSC workshop will be hosted by two teachers, Johan van Kreij and Lex van den Broek. The course is mandatory for the Sonology Bachelor 2 (B2) group and it will consist of two intensive workshop weeks (2 x 5 days), one in the autumn and one in spring. During these workshops we will talk about sensors, actuators, coding, digital-and analog- electronics and we will guide the participants with their Musical Controller Project assignment.

The goal of the workshop is to discover more about the the technology behind musical-instruments and controllers and to be able to design and create your own instrument and play it!

CourseDates 22-23:

introduction day #1 Tuesday October 4th, 15:30-17:30
introduction day #2 Tuesday October 11th, 15:30-17:30

WorkshopWeek 1: 11 – 15 November 2022
WorkShopWeek 2: 13 – 17 March 2023

Sensor Overview (day 1)


Introduction to Electronics Ba1

Academic year 2022-2023

Introduction to Electronics Ba1

Introduction to Electronics” for Sonology Ba1 students consists of at least 6 group lessons with an additional small electronic assignment to finish the course. In these lessons we will talk about the most fundamental electronics subjects like: ohms law, AC, DC, frequency, phase, digital, analog, interfacing, sensors, building electronics, power supplies and much more. Also subjects that come along with all the questions you have during the lessons will be part of the content.

Please check the content of this website as well for more information about the different subjects. Check the video page for some fundamentals. The lessons will start Tuesday October 4th in Sonology studio 6.75 (studio for live Electronic music). Check your Asimut agenda.

Assignment for this course (22-23)

Build your own small electronic device that works

At the start of the first lesson you will all get your own small electronics-kit that consists of the following components:

A small breadboard,
9V battery, battery clip,
Resistors: 2 x 10k, 2 x 470k, 2 x 470E
Capacitors: 1 x10uF, 2 x 100uF, 2 x 10nF, 2 x 100nF
Leds” 2 x Red, 1 x green
Semiconductors: 2 x NPN (BC547), 1 x PNP (BC557), 1 x FET (BS170)
A few wires

Electronics Starter package

Below you see the PDF ‘booklet’ of the ‘Electronics starting kit” which we will use during the lessons as a nice starting point for building some simple electronics.



A capacitor is a passive component that consists of two metal (conducting) plates that are separated by a material called a dielectric. This dielectric is an electrical insulator that can be polarized by an applied electric field. The positive and negative particles inside the dielectric are not polarized if there’s no voltage applied.

The capacity of this component is measured in Fahrad. Common values in audio world are between 1pF – 10.000uF. When a DC voltage is applied to both sides of the capacitor, the capacitor will charge (look at the moved particles). For a very short time (time = 0) there will be a current flow that charges the capacitor. After the capacitor is charged, there will be no current anymore – until you change the polarity.

The capacitor is a super small chargeable battery.

Important to remember:

for DC voltages, the capacitor is a huge resistor or a blockade.

When an AC voltage is applied, the result will be different! Because of the changing direction of the current, the capacitor will be charged positive and charged negative and it will conduct the current in both ways. In other words: for ac-voltages (audio signals for example), the capacitor is a conductor. See the animation below.

for AC-volatges, the capacitor is a conductor

Building electronics

Building Electronics ‘tips’

When you want to make your own electronic device for the first time ever, you will encounter some challenges. How do you start? How can you make electronics stable and reliable. On this page some fundamental tips to help you create your own device.

Try to build the board or circuit ‘modular’. Do not build all parts of the circuit at once and on the end of the line connect the power, finding out it does not work. This can be very frustrating. Test your circuit while you are building. Build small sub-parts of the total circuit and test them separately.

Connect (or route) the power supply of the circuit first. Add functionality later. Try to use wire color consequently, especially for power connections: Red for plus power supply, black for ground, and blue for negative power supply. This way it is easier to check for mistakes. If you do not have these colors available, try to stick labels to the wires.

Use the right cable for the right purpose: Thick(er) cable when the current is expected to be high (think of big speakers). Use shielded cable when the signal is very weak and/or high frequent. When you think the wire will move around (or vibrate), choose a cable that is flexible so it wont’ break.

Always build safe. Officially, by rule, any voltage above 48V is considered dangerous. When you are working with 230V~ AC, make sure no finger can touch /reach these voltages. Use good isolation and always be ‘aware’ of this lethal potential energy.

When touching 230V~AC, it’s the frequency in combination with the high voltage that’s dangerous. Our heartbeat is about 60 times per minute; one time per second. The frequency of the net is 50Hz; 50 times per second  … 

Building a Printed Circuit Board

Proto typing example

Below an example of how to transfer an experimental circuit (a simple audio amplifier) into a stable printed circuit board.

The circuit – LM386 audio amplifier, with an input volume potentiometer, an output filter, speaker and powered by a 9V battery.
The circuit build and tested on a breadboard.
Place the component(s) on the right position. This side of the board is called the ‘component-side’.
The other side is called the ‘soldering side’. This side has soldering pads, where the pins of the components are fixed (soldered).
More components placed on the top-side – choose a practical location on the board, thinking ahead of how the connections below have to be routed.
Cut the wires on the bottom side.
Be aware of the fact that the connections are ‘mirrored’ when compared to the top-side.
Connect the points with iron wire to realize the circuit. It’s a good idea to use thicker wire for the GND connections.
Place some ‘male-headers’ to have the possibility to connect the wires.
Make the connections complete on the bottom-side.
Connect the wires , the battery and the speaker,
The backside, or soldering side complete.

How to connect ‘Ground’

When you connect power to a circuit, use thicker wire for the ground. The ground should always be very LOW IMPEDANT. This means, the resistance should be low. Thicker wire does the job …

Think of the water supply in your house: the water is entering your house through a tube of 14mm, but going out in a big tube. In other words: using thicker wire for the ground, avoids disturbances and unpredictable behavior. Also check how you connect the ground.

A simple setup of a circuit with “A” being a circuit or a component connected to the power.
Connecting a circuit like the example above can cause ‘noise’ problems. The ‘dirty’ ground from process C is polluting the ground of process A and B. Always make sure that the ground of a certain process (this can be an opamp, a motor or other electronics) has a separate ground connection … 
Always try to connect the ground into a star
If connecting the power to a circuit, it’s a good idea to add a capacitor. This will function as a LowPass filter; it will take away disturbances.

Components and (european) symbols

Electronics is great and it is all about the control of currents and voltages in a circuit. By using the right components with the right value in the right order, the most fantastic applications can be created. Let’s start looking closer to the symbols that are used when we talk about components in a circuit.

Common symbols/components

European symbols

Starting with the generic symbol of a battery, or a DC-power supply. The “+” indicating the positive connection and the “-” the minus or zero. Often the zero is also referring to ‘ground’. This is the fundament of a circuit: the power supply.

A line is referring to a wire which is a electrical connection between multiple points in a circuit. When two lines cross, a dot indicates a junction – there is a connection. When two lines in a circuit diagram cross without a junction – there is NO connection.

There are a lot of different symbols indicating ‘Zero’ or ‘Ground. The symbol with the 3 lines is indicating earth literally. A connection to the physical ground. Ground (zero) is a reference.

Capacitors are simple passive devices that can store an electrical charge on their plates when connected to a voltage source.
Read more …

A resistor is a component indicating ‘resistance. The bigger the resistance, the smaller the current through the resistor. Resistors can have many differents packages. In general 1/8 watt resistors are used in audio circuits referred to in this website. The value of the resistor is indicated with colored rings. Check this link for the values.

Switches can be found in lots of packages or configurations. A switch creates a connection (ON) or an infinite resistance (off).

The common symbol for an amplifier is a triangle. It is not referring to specific type, but a general indication that a signal is ‘amplfied’.

A coil is a a long wounded wire (around a core) creating resistance for higher frequencies. Therefor coils are mainly used in filters.

An Operational Amplifier, abbreviated opamp. This ideal electronic building block has an inverting and a non inverting input and one output. Check this page for more details.

A potentiometer is a variable resistor.

A diode conducts current in one way only – therefore its symbol looks like an arrow. The “A” indicates the Anode (positive) and the “C” the Cathode (negative). The diode with the two arrows indicate a Light Emitting Diode or LED.

One of the most important components of ‘modern’ electronics is the transistor. The transistor exists in many different shapes. The most common ones are NPN and PNP. Check this short movie of the transistors for more details.

A Field Effect Transistor or FET. The bg difference between a transistor (BJT) and a FET is the way it is driven. a transistor is current driven and a FETis voltage driven.

Oscillator principle

Oscillators with CMOS HEF 40106

An oscillator is an electronic circuit, that produces a repetitive electronic signal.
During this last lesson we will experiment with some some simple oscillators. Take a look at the animation on the right. This shows the resonance of a spring/mass combination, in an ‘undamped’ setup; so no losses due to friction. An electronic oscillator is more or less the same. A resistor (R) in combination with a capacitor (C) will also resonate. If we connect the R and the C to an active component (giving it energy to resonate), we have an oscillator.

Let’s take a look at the active component that we are going to use: a CMOS invertor, the HEF40106. This is an Integrated Circuit (IC) with six inverters in one package. The 40106 is also called a Schmitt-trigger, because of it’s hysteresis between the in-and output.


The circuit above shows the simplest setup of an oscillator. How does that work? Pin 2 (the output of the inverter port) is connected to the input of the same port through a resistor R. The input is also connected to a capacitor.

How does that work?
– Suppose the input at pin 1 is 0V (in case of start-up for example), the output will be ‘high’. If the power-supply of the chip is (say) 9V, the output is also 9V.
– At that moment the voltage at pin 2 is higher than pin 1, the current will flow through the resistor R, into the capacitor C.
–  The value of the voltage parallel to the capacitor will ‘slowly’ rise above the upper threshold and the output of the invertor will switch from 9V to 0V. Now the capacitor will discharge through the resistor, until the value of the input (pin 1) will drop below the lower threshold – the output goes ‘high’ again (it will be 9V).
– We are back at the beginning and the cycle will keep on going. It will resonate its own static frequency. The frequency depends on the value of the capacitor and the resistor. They determine the ‘speed’ of the proces.  The bigger the capacitor and the resistor are, the slower the system resonates, the lower frequency will be


Based on the principe explained above, there are lots of variations on the same theme. The circuit below has diodes in the feedback part, which will create different pulse width’s.

Master and Slave

The circuit shown is called a master-slave combination. The ‘ slave’ is only active when the output of the  ‘master’ is ‘high’, due to the diode. The capacitor and the resistor of the master have higher values and will resonate on a lower frequency. The ‘slave’ has smaller values and is oscillating on a higher frequency. On pin 4, the output of the slave, the ‘master envelope’ is filled with the signal of the slave. Both resistor symbols do have an small arrow. This means you can use ANY variable resistor you want (LDR, FSR, Potentiometer, Digital potmeter, NTC, …).


While making all the projects, I’ve been using a lot of different Opamp circuits and actually the basic concept of the circuits used, is often the “same”.  In this article I will point out the most important Opamp circuits used in combination with active sensors. These active sensors, like for example the acceleration sensor, produce a tiny DC-voltage change, which has to be amplified and tweaked.

Some fundamentals:

The word “Opamp” is an abbreviation of ‘Operational Amplifier’ and is an ideal building block in electronics. There are 3 fundamental properties:

1. It has a very high input impedance (resistance): so it doesn’t take any current into it’s input.
2. It has a very low output impedance; so it can deliver a relative strong output current.
3. The amplification (Au) is very, very high.

In the circuits below, the power supply of the Opamps is not drawn. If you make use of an opamp, you will always need a power supply to ‘feed’ the opamp. Most of the times, especially in audio world, the opamp needs a balanced power supply, meaning +voltage, ground and -voltage. When I work with sensors, I do use  Opamps that also work with a single power supply (+voltage and ground). For example: LM358, TLC274, LM324. For more information about the opamp itself, checkout the wikipedia or equivalent websites.

Follower or Buffer circuit:

This circuit is used to ‘buffer’ the output of a sensor. Often the sensor is placed far from the actual sensor interface, so long wires have to be connected to it. To avoid loss of the signal (the output of the sensor is not always capable of generating enough current), this circuit can be applied. The output of the sensor is connected to the positive input of the opamp. Because of the feedback from the output to the negative input, the Au (amplification) is 0dB, or 1x. The output signal is not amplified, but just ‘follows’ the input. The opamp is capable of driving more current and a somehow longer cable will not be a problem. The sensor just has to deliver it’s tiny current (almost zero!) to the input of the opamp.

The graph on the right shows the input- and output signal of the follower-circuit. Both the amplitude and the phase of the signals are the same.  Note the blue and red line. They represent the power supply lines which are connected to the opamp and thus representing the maximum Vtt (voltage top-top) the opamp can generate.

Non-inverting amplifier

The non inverting amplifier has an amplification which is always more than 1x (>0dB). The proportion between the both resistors Rf (R feedback) and R1 determines the amount of amplification. The output of the sensor is connected to the positive input of the opamp.

In formula: (Uout/Uin) =  Au = (1+ Rf/R1)

The graph on the right shows the in- and output signal. The amplitude of the input signal is amplified. Note the distorted signal on the right! If the amplification (proportion of the both resistors) is higher than the maximum output swing of the opamp (Vtt), the signal will ‘clip’ and the shape of the signal will change (be distorted).

Inverting amplifier

The amplification (Au) with the inverting amplifier only depends of the proportion between Rf (R feedback) and R1. The output is 180 degrees out of phase with the input; it’s negative. This circuit is also known as the summation amplifier.

In formula: (Uout/Uin) = Au = – (Rf/R1)

The graph show the output signal inverted, it is 180degrees out of phase with its input. Also here, too much amplification can cause distortion.

Non inverting amplifier with offset adjustment

A lot of sensors do generate a little DC-voltage change, but do have some DC-offset on the output. With the ADXL202 chip for example, the filtered output is “DC-change”  (=AC) in reference to 2.5V.  When the sensor is tilted to one side, the output will be 2V and tilted to the other side 3V. This means a maximum change of 1V. It would be better to have the output swing a big as possible – a higher resolution. In the circuit above, the amplification will be around 2,5 -3 times (around 10dB). With the potentiometer connected between the plus and minus power, the output DC-offset can be adjusted to zero.

In the picture on the right a graphical representation


What is Electronics?

Electronics is an absolute fascinating world with the possibility to create any circuit and any functionality that you would like. But bear in mind: electronics can be very complex and frustrating as well. Circuits that do not work. Components that smell funny or circuits which are unstable. How do you cope with that? Let’s start with the fundamentals of electronics:

Wiki definition: Electronics deals with electrical circuits that involve active electrical components such as transistors, diodes and integrated circuits, and associated passive interconnection technologies. The nonlinear behavior of active components and their ability to control electron flows makes amplification of weak signals possible and electronics is widely used in information processing, telecommunications, and signal processing

Electronics is about the control of current in a circuit. If the current somewhere in the circuit is too small, it is not stable or not reliable. If the current too high, the temperature will be too high. It has to be somewhere in the middle. These lessons will give you a complete introduction to Electronics. We will focus on the basics and fundamental circuits that are applied in music and art. We will talk about the common applied components, passive and active and also the small programmable computers (Arduino, Teensy), or sensor interfaces will be part of the subjects.

Electrical current

All materials you can imagine are made out of atoms. The core of an atom is the nucleus which has protons and neutrons. In the outer shells there are electrons. Check the picture below.

Materials that do not conduct current, like wood, glas or plastic do not have free electrons, because the nucleus with positive particles is in balance with the negative electrons. Materials like copper, gold or metal are not in balance. They have more electrons in the outer shells which are not linked to the positive nucleus – this means they are free to move through the material. We have free electrons and thus: conductance.

When you think about current through a wire, you can imagine electrons like marbles (or water), that are pushed through a pipe (see image above). Electrical current is measured in Amperes. If the current is one ampere (1A), it means that in one second 6,242*1018 electrons pass a given point. The more current flows through a wire, the thicker the wire should be. Check the video section of the webiste.

The amount of current (Ampere) through a wire is determined by the applied Voltage (V) to that wire and the amount of resistance (Ohm) of that wire. This brings us to Ohms law. See lesson 1


The behavior of current and voltage in a circuit is defined by the two laws of Kirchoff:
Kirchoff’s first law:

For any node (junction) in an electrical circuit, the sum of currents flowing into that node is equal to the sum of currents flowing out of that node.

This means that the current entering any junction is equal to the current leaving that junction. In math:  i2 + i3 = i1 + i4

Kirchoffs’s second law:

The directed sum of the potential differences (voltages) around any closed loop is zero.

The sum of all the voltages around a loop is equal to zero. In other words:
v1 + v2 + v3 +v4 = 0

AC and DC

AC stands for Alternating Current. The value of the signal changes polarity over time with a certain frequency. The AC current will move both ways – back and forth.

DC stands for Direct Current. This means that the voltage does not change polarity over time. It is a straight line in the figure. Think about a battery. The plus (+) and minus (-) indicate you are dealing with DC. The current in the wire will move in one direction only.


The frequency of a signal defines the amount of changes per second and is measured in units of Hertz [Hz]. So if we have an AC signal that changes (polarity) over time, this signal has a certain frequency.

Looking at the figure below you see a representation of a sine-wave. The circle on the left represents a rotating point (think of the pedal of a bicycle) – with starting at point “A”. The point rotates left and will go up towards point “B”. If we would draw the position of the moving point in time, we will see the first 90 degrees of a sine-wave. Following the pedal from “C” to “D” and back to the beginning at point “A”, we see a full sine-wave (360 degrees). This one full circle is also called one cycle (T). The variable T indicates the cycle time in seconds.

The amount of cycles that fit into one second (1 sec) is called the frequency F. So if we talk about a frequency of 1kHz (=1000Hz) this means that this signal makes 1000 cycles in one second.

Written in formula this looks like this. The smaller the cycle time , the higher the frequency.


The Amplitude, often indicated with “A” is a value for the “strength” of a signal. The Peak to Peak Amplitude (A2 in the figure) is the change between the two ‘peaks’ of the sine-wave – the maximum swing.

If you want to measure the average value of the sine-wave, this is called the RMS value of the Amplitude. (A3) The multimeter shows the RMS-value.


A mono signal cannot have ‘phase’, because phase is referring to a time difference between two repetitive signals. A sine-wave and a cosine-wave for example have a phase ‘angle’ of 90 degrees ( = 1/2π).

When two speakers are connected to an amplifier the correct way, both loudspeakers move forward and backward exactly the same time – the waves are ‘in phase’. If the connection of one speaker is then inverted (minus and plus swapped) we introduce two speakers that are ‘out of phase’. Check the waves below.

Electronic filters are created with time dependent components like capacitors or coils. When we connect an ac-signal (audio signal) to the input of a filter we can compare the in- and output to determine the ‘phase angle’ between both signals. In the figures below a positive- and negative phase example.

Positive phase angle
Negative phase angle

Power Supplies

Power supplies

Working with electronic-circuits means you are always in need of ‘power’. A lot of circuits work with battery operated power. This is not really dangerous and if the battery ‘dies’ on you, you just buy a new one. But for a lot of reasons (environmental, money, more power) it’s a better choice to make use of power-supplies.

A power-supply takes its energy from the wall-socket (in Europe 230V AC/50Hz / USA and Japan 110VAC/60Hz) and converts this into low voltage DC.  So before we have a power-supply that provides us with (let’s say) +9VDC, there are some important steps to take.


The first thing is to transform the 230V~ (Europe) down to (for example) 12V~. This is done by a transformer. A transformer is in its fundamental a piece of metal with two coils wound around it. See the picture (thanks Wiki).  The red wire is the primary winding and the blue wire is the secondary winding.

The red wire is connected to the mains (230V~) and is inducing a magnetic Flux within the metal core (green dotted line). In the blue wire, wound around the same metal core, an electric current will flow (induced) because of this magnetic flux. If the amount of windings on the primary side (N1) is equal to the amount of windings of the secondary side (N2), the voltage on the input and output are equal. But let’s say the primary coil has 1000 windings and the secondary coil has 100 windings, the output voltage (the secondary voltage) will be 23V~ (230 * 1/10). So the proportion of the primary and secondary windings ( N1/N2) determine to which value the voltage is transformed. In practise there are values that vary from 6V~, 9V~, 12V~, 15V~, 18V~, 24V~, … Note that the output (~) is still an AC signal. It has a smaller amplitude but it still has the same frequency (50Hz).

Important notice is that a transformer only works for AC! 
Since the coil is just a long wire, it’s (dc) resistance is low and when a DC-voltage is applied, the current will be too high (the coil can burn). For AC-signals a coil acts as a resistor, so for AC the current will be low(er).
The other reason why only alternating signals works for a transformer, is that we need alternating current to create a constant changing magnetic field (flux). Due to this changing magnetic filed, a current will be induced in the secondary coil.


The next step in the design of a dc-power-supply is to ‘rectify’ this low secondary AC-output of the transformer and change it into a DC-signal. This is achieved with the use of 4 diodes actually placed into a bridge-circuit, also called Greatz circuit. These 4 diodes connected to an AC-signal will double rectify the AC-signal. If a big capacitor is placed parallel to the output of the diode-bridge, the rectified output will be smoothed and the ‘gaps’ between will be filled. See the figure below.

Voltage regulation

The setup above shows the very standard and simple power-supply setup. The DC output of this setup still has some ‘ripple’ (= dsiturbance) on top of the DC signal (see the ‘capacitor’ part of the graph). To make a ‘perfect’ straight DC output, we make use of so called regulators.

Regulators, like the ‘7809’ in the example above,  do come in all kind of forms or shapes. The 78XX series are positive regulators and the number (XX) determines the value of the voltage they will regulate. Of course this is only possible if the voltage in the input is higher than the regulated output. In general the difference between the in- and the output should be at least 2,5V. The capacitors used on the in- and output of the regulator are here to avoid oscillation and they are placed as near the regulator as possible. The power supply with only +9V output is also called a ‘unbalanced’ power supply. It is only one value.

If you want to work with audio circuits you most likely need a balanced power supply. This is a supply that provides you with both plus and minus values. An example below:

Single sided power

Unbalanced power supply

When you are in need to power your circuit, most of the time you will use a battery (or a powersupply as decribed above). A single battery provides you with only (for example) +9V DC in relation to the 0V – hence the plus and the minus connection. Take a look at the picture below.

For a lot of circuits this single battery will be fine. It can provide the circuit with 9V and a small current of (more or less) 100mA. If you want to power an audio circuit (opamps for example) with only one battery, then you will encounter a challenge. An audio signal (AC) is positive AND negative! If you think about a speaker that generates sound, the membrane of the speaker will move forwards but also backward – through the zero (rest) point. See the picture below with a speaker moving forward (+) and backward (-).

A circuit that amplifies an audio signal needs to have ‘balanced power’. A single-sideded powersupply (like a battery) can not provide this- it is only positive. If you would connect an audio amplifier to a single sided powersupply, the picture below shows what will happen:

The negative part of the sinewave cannot be amplified, because there is no negative power! So how can we make sure that the negative part of the sinewave will be amplified as well? The answer: use a balanced power supply. This is a power supply with two sources, placed in series.

Double sided power supply

Balanced power supply

If we take two batteries (or voltage sources) and place them ‘in series’, we actually create 3 points. We have the plus, the zero and the minus. In general plus (+) is indicated with red, ground or zero with black and negative (minus) with blue.

IF we now want to amplify a sinewave, we have positive AND negative power available and the audio signal can be streched up and down. See the graph below.

Create simple balanced power

There is also a possibility or ‘trick’ to avoid the use of two power sources or batteries. Like explained in the fundamentals and ‘Ohms law’, you can also create a voltage divider with two resistors. The two resistors divide the voltage in two equal parts, e.a. 9V divided by two creates two times 4,5V. See the image below:

The middle point (0V) can now be used as ‘ vritual ground or ‘signal ground. In reference to that point you have +4,5V and -4,5V. We have balanced power. The signal-ground (virtual ground) should not be mistaken for the real ground. It still has a potential voltage of 4,5V. Circuits tat make use of this setup always have to apply a capacitor to get rid of the DC component.

Ohms law

Ohms law

Some basics of electronics

To be able to understand a bit more about electronics and the circuits that are shown on this or other websites, it is actually inevitable to understand Ohm’s law – it makes live a bit easier. You have to understand what happens with the current, the voltage and the resistance. All these three variables are linked and make part of  ‘Ohms Law’.

In formula:  U = I x R  

The voltage  [V] is a product of the current {A] times the resistance [Ohm])

A graphical representation of this formula: when you look to the triangle from one of the three angles, you ‘see’ the formula’s for every variable. If you look from the top you ‘see’ U = I*R. Looking from the left corner beneath, you ‘see’ I=U/R.

In other words: the higher the value of the resistor, the lower the current given a constant voltage (the battery). If the resistance is 0 Ohm, we call this a short-circuit. A short circuit will result in a undefined value (too high) of the current (dividing by zero is not possible)

Suppose you have a battery of 9V. If you connect a resistor of 1kOhm (=1000 Ohm) parallel, the resulting current will be:
I = (U / R) = 9 / 1000 =
9 mA = 0,009 Ampere (A) (9 mili Amp)

Within electronics, the values we use will vary from Tera (= 1000000000000) or 1012 ( a one with 12 zero’s) to pico: 0,000000000001. The engineering values always take steps of ‘3’ digits, in order to keep the notation clean and avoid errors.


Voltage divider

If resistors are placed in series (see figure below), the total resistance is a summation of al the resistors. So the total resistance in the example below is: R1+R2. If more resistors are placed in series, just add them up. If you have the total resistance, the current can be calculated in that circuit with ohm’s law.

The current (I) in the series-circuit (see above) is the same in the whole circuit. There is only one branch. The voltage however is divided into equivalent parts. Another name for the circuit above is a voltage divider. The current through a resistor causes a ‘voltage-drop’ so with two resistors the voltage is divided into two values. If the series resistors have the same value (let’s say 1k), the value of the voltage parallel to the resistors is the same – the voltage is divided in equal parts. In case of the example below, the 10V of the power-supply is divided into two times 5V.

Be aware of the values that you use with these kind of calculations. Try to make use of the ‘engineering-values’ and avoid shifting comma’s. See the figure below.

If we would look at the series circuit defining an input and an output, the battery is the input and the voltage parallel to R2 is defined to be the output. This is an important definition when we start to talk about filters!

The output of this series-circuit can be defined like this:


Current divider

If resistors are placed parallel (see figure below), they divide the current in equivalent parts – hence the name current divider. The voltage parallel to the two resistors is for both resistors the same – it is one electrical node (= electrical point). The current however is divided into two separate current flows. The amount of current is determined by the value of the resistor. See the figure.

The total resistance of parallel resistors is the inverse of the series switched resistors. To calculate the total resistance you have to sum the inverses. This means that when resistors are connected parallel, the total resistance will go down. Suppose we have 2 resistors of 1kOhm placed parallel, the total resistance will be 500 Ohm.

Quiz question 🙂

Below a circuit with series and parallel connections. The voltage of the battery is 10V dc. All resistors have the same value of 1K Ohm. The quiz question is: what is the voltage parallel to resistor R4? Good-luck!

PS: the symbol on the bottom of the circuit indicates the ground connection.