Time Constants Tutorial

Like charges repel, unlike attract.  In the first diagram, when the switch is closed, the negative terminal of the battery repels the negative electrons and pushes them onto the upper plate of the capacitor C.

Similarly, the positive terminal attracts the negative electrons away from the lower plate. If the battery is now removed, C remains charged up to the battery voltage. This can be dangerous, since capacitors can remain charged to high voltages for a long time. If a screwdriver is now placed across the capacitor terminals, the surplus electrons on the upper plate will now flow to the lower plate.
The C is now discharged.
Doing this can also be dangerous.
The screwdriver has a low resistance, and Mr Ohm says "low resistance means high current". One vapourised screwdriver !!
Therefore large, highly charged capacitors must be discharged via a resistor, to limit the amount of discharge current that can flow.
In the second diagram, a resistor R has been placed in series with C. When the switch is closed, C charges from the battery, as described previously. The charging current passes through R. Since R limits the amount of current that can flow (Ohms law), C takes time to charge up to the battery voltage.
The larger the values of C and R, the longer C takes to charge. Liken it to filling a bucket with a hosepipe. The larger the bucket (C), and the more you stand on the hosepipe (R), then the longer it takes to fill the bucket. The value of C in Farads, multiplied by the value of R in ohms, gives us the TIME CONSTANT (RC), measured in seconds.

If C = 2 Farads and R = 10 ohms then RC = 20 seconds. This means that C will take 20 seconds to charge up to 63 % of the battery voltage. If it is a 100 volt battery, then after 20 seconds, the capacitor voltage will be 63 volts.
If we draw a graph of the increase of capacitor voltage against time, then we get a curve that is not linear ( not a straight line).
The curve is exponential. It increases rapidly at the start and then slows down. It gets slower and slower.

If C is discharged, by connecting a resistor across it, then the capacitor voltage falls BY 63 % after RC seconds.
Time constants are often used where a time delay is required.

What is Phase Tutorial

The generator at the power station which produces our AC mains rotates through 360 degrees to produce one cycle of the sine wave form which makes up the supply.

In the next diagram there are two sine waves. They are out of phase because they do not start from zero at the same time. To be in phase they must start at the same time.
The waveform A starts before B and is LEADING by 90 degrees.
Waveform B is LAGGING A by 90 degrees.

The last diagram, known as a PHASOR DIAGRAM, shows this in another way. The phasors are rotating anticlockwise as indicated by the arrowed circle.
A is leading B by 90 degrees.
The length of the phasors is determined by the amplitude of the voltages A and B. Since the voltages are of the same value then their phasors are of the same length. If voltage A was half the voltage of B then its phasor would be half the length of B.
All this has nothing to do with "set your phasors on stun".

The RF Spectrum Tutorial

Frequency Range	Classification
3 - 30 kilohertz30 - 300 kilohertz 300 - 3000 kilohertz (3 megahertz) 3  - 30 megahertz 30 - 300 megahertz 300 - 3000 (3 gigahertz) 3 gigahertz - 30 gigahertz 300 - 3000 gigahertz	Very low frequencies (VLF) The long wave band (LW) The medium wave band (MW) The short wave band (SW) Very high frequency band (VHF) Ultra high frequency band (UHF) Super high frequency band (SHF) Microwave frequencies

Higher in frequency than this are infra red, visible light, ultra violet, X rays etc. which are all forms of Electro Magnetic radiation.

The Integrator Tutorial

We suggest you read the TIME CONSTANTS before tackling this one.
The integrator consists of a capacitor and resistor connected as shown.
A PULSE TRAIN is applied to the input.
When an input pulse rises rapidly to maximum the capacitor charges exponentially through the resistor as shown in the lower waveform.
When the input pulse falls suddenly to zero the capacitor discharges exponentially to zero. The process is repeated for each pulse giving the waveform shown.

The Differentiator Tutorial

Read the page on TIME CONSTANTS before trying this one.

The differentiator is made from a capacitor C, and resistor R, and assembled as shown. A PULSE TRAIN is applied to the input.
When a pulse of voltage rises suddenly from zero to maximum, the current which is charging C suddenly rises to a maximum value as well. As C charges, the charging current falls exponentially to zero.
Since this charging current is passing through R the voltage across R (which is the output voltage) does the same. Therefore we get the shape shown, with the voltage out rising suddenly to maximum and then falling exponentially to zero.
When the pulse falls to zero C discharges. The discharge current is high at the start and then falls exponentially to zero as C discharges.
However, since the discharge current is in the opposite direction to the charge current the voltage across across R will be reversed and so the waveform is now shown below the zero line. For each pulse the waveform out is repeated giving the display shown.
Ohms Law says that current is proportional to voltage. Conversely, voltage is proportional to current.

Source and Load Tutorial

The SOURCE is a source of power. The LOAD is powered by the source. Two terminals on the source are connected to two terminals on the load.

SOURCE	LOAD
battery amplifier output microphone motor  dynamo	amplifier loudspeaker amplifier lathe lamp

Current flows out of the source through one lead, through the load and then back to the battery via the other lead.
The value of the current flowing back to the battery is exactly the same as that leaving. Nothing is lost or gained.
To protect the load and source against excessive current flowing due to a fault, a fuse is inserted in one of the leads.

Sound Tutorial

• Sound waves are caused by vibrations such as that from a tuning fork, a loudspeaker cone, or the human voice.
• These vibrations need air to travel through. They cannot travel through a vacuum.
• The air itself doesn't travel.
• The sound causes compression and decompression of the air as it moves through it.
• There is a regular spacing between one pressure peak and the next.
• This distance is called the WAVELENGTH.

• Sound travels at about 330 metres a second.
• A pure sound tone consists of a single frequency of vibration.
• The range of human hearing is about 20 Hertz to 20 KiloHertz.
• Most sounds are a mixture of frequencies. See the page on HARMONICS.
• Microphones convert sound pressure waves into electrical signals.
• Loudspeakers convert electrical signals into sound waves.
• Loudspeakers and microphones are TRANSDUCERS.
• Frequency, wavelength and the speed of sound are interrelated.

Wavelength x frequency = the speed of sound in metres per second.