References

• The Great Power vs. Energy Confusion, Rob Lewis.
• Electric potential energy, Khan Academy.
• Essential & Practical Circuit Analysis: Part 1- DC Circuits, Solid State Workship, YouTube.

Conventional Current And Charge

Historically positive charge moves through the circuit from the positive to negative terminals. This is called conventional current. We now know that it is, in fact, the flow of electrons from the negative to positive terminals that is current. Due to the historical precedent, current is still often shown as conventional current.

From Wikipedia: Conventional current flows from the positive pole (terminal) to the negative pole. Electrons flow from negative to positive. In a direct current (DC) circuit, current flows in one direction only, and one pole is always negative and the other pole is always positive. In an alternating current (AC) circuit the two poles alternate between negative and positive and the direction of the current (electron flow) reverses periodically..

Note that voltages are relative, which is why the negative terminal of the battery can be negative - it depends what the reference voltage you are measuring agains is - e.g. if ground is midway between the two terminals then they will have voltages -A and +A respectively.

Informally, current is a flow of electric charge.

Current, , is the amount of charge, , that moves through a point in the circuit at any time. Charge, , is measured in Coulombs. One electron has a charge of Coulombs. This is the smallest unit of charge possible.

Voltage

Voltage, , is the amount of work (in Joules) that must be done per unit charge to move between two points in a field. I.e. 1 volt is 1 Joule per Coulomb.

To help understand this let's revisit the terms energy, work and power.

Energy is the ability to do work.
Work is the force that must be exerted to move a mass a certain distance.
Power is the rate at which energy is generator/consumed.

Energy is what makes it possible to move things. Moving things involves doing work and it takes energy to do this. Energy measures the total amount of work done. It does not say how fast the energy was used/produced.

Power gives that rate at which energy is used/produced. Power measures how fast the work gets done.

Give these definitions we can see how they are defined for electronics. Using some crude (read incorrect as we're using multiplcation not integration to make it seem simpler) we see: So energy is indeed the total work required to move a charge between two points in an electric field. And because We can see that electrical power (measured in Watts) is the rate of consumption/generation of electrical energy.

Note that electric potential energy is measured with respect to a reference point. In the image below one can see that the voltage either side of the resistor is measured w.r.t ground. Ground is the normal reference point, but any point in a circuit can be used as long as it is used consistently.

Note then, that potential difference, is the difference between to points, each of which has a potential energy w.r.t to a reference. The potential difference is the difference between these two points, but only make sense if the potential of each point is measured w.r.t to the same reference.

Ohm's Law

Kirchoff's Laws

Nodes, Branches and Loops

Branch: A branch represents a single element such as a resistor. I.e., any two terminal element.

Node: A node is the point of connection between 2 or more branches. Every point going into the node, at the node, is at the same potential.

Loop: A loops is any closed path in a circuit. Starts and ends at the same node and does not pass through a node more than once.

The Laws...

Two important laws: Kirchoff's voltage law and Kirchoff's current law.

KCL

Kirchoff's current law says that the sum of currents flowing into a node must equal the sum of currents leaving a node. This is often expressed in another way: the sum of currents entering and leaving a node must always be zero. This works because we label, by convention, all currents entering the node as positive and all currents leaving the node as negative.

This can be written most compactly as:

Lets look at the following example [Ref]:

KVL

Kirchoff's voltage law says that the sum of voltages around a closed circuit must be zero.

This can be written most compactly as:

Say, for example, that is 12V, R2 is , R3 is , is 3V and R5 is . Then we know . We can then work out the current in the circuit using KVL by re-arranging the formula.

Resistors control the current that flows through a part of a circuit, as described by Ohm's Law (). Using the formula one can see that as either resistance increases, current falls, and vice versa.

Resistor Colour Codes

Resistor's In Series

Resistor's In Parallel

Voltage Divider

Current Divider

The Wheatstone Bridge

Power

Voltage Sources

Current Sources

Source Transformations

Superposition

References

Switches are defined by the number of poles and throws they have...

Poles: A switch pole refers to the number of separate circuits that the switch controls.

Throw: The number of throws indicates how many different output connections each switch pole can connect its input to. Think of it as how many places a single source can be "thown to".

A capacitor consists of two conducting plates separated by an insulator (a.k.a. a dialectric).

When connected to a voltage source, the source creates a positive charge on one plate and a negative one on the other plate:

Charge stored is proportional to applied voltage: Where is called the capacitance of the capacitor and is measured in Farads (F). By re-arranging the above we can see that capacitance is the charge per volt that the capacitor can store. Thus, the more charge that the capacitor stores per volt, the higher its capacitance is. This quanitity is dependent on the type of dialectric used, the surface area of each plate and the distance between the plates.

Recall that current is the amount of charge that moves past a point per unit time. Thus, by differentiating w.r.t time, the above, we get the current-voltage relationship of a cap: This gives us in important property of caps. Because for DC current the voltage does not change, is zero, so a capacitor is an open circuit to DC! (But it does charge). Because of the definition of a derivative, we also know that the voltage across a cap must be smooth - i.e., it cannot change abruptly.

Note that real capacitors dissipate their energy over time - they "leak"

Capacitors resist abrupt changes in voltage, which is why the function as low pass filters.

Charging Through A Resistor

When a capacitor, with a capacitance , charges in series through a resistor of resistance ohms, in seconds it will charge to 63% of the supply voltage and in seconds it charges to over 99% [Ref]. You get an exponentially decreasing current flow as the resistor draws current from the battery and the capacitor stores the current's flowing charge [Ref].

Recall KVL: the sum of voltages around a closed circuit must be zero. The dotted arrow in the diagram above shows a direction around a closed ciruit, which by KVL means that [Ref]: I.e., the current at time is proportional to the difference in voltages across the supply and the capacitor, the constant of proportionality being the resistance.

Now a quick aside to derive something we're going to need:

Recall: If we differentiate w.r.t time, we get: And we know that , so we can write: I.e., the current at time is also proportional to change in voltage across the capacitor, the constant of proportionality being the capacitance.

Now we can continue by substituting into to get: TODO - FILL REST IN

We end up with: We can see that as the value of RC increases, the exponential value will decrease, which means that the time it takes to charge the capacitor increases with either , or both of, and .

Capacitors In Series

Capacitors In Parallel

References

• Capacitor i-v equation in action, Willy McAllister, Khan Achademy,
• Derivation of Charging and Discharging Equations for RC Circuit, Khan Achademy,
• Deriving the formula from scratch for charging a capacitor, Adam Haun's answer on StackOverflow.com,

An inductor is a coil of wire, sometimes round a feris core, that stores energy in its magnetic field. Its strength depends on the number of turns in the coil and the type of core material and its cross-sectional area.

Inductors oppose the change of current flowing though them. They are measured in "Henrys". The formula below defines inductance, L. Inductance is the voltage generated per unit change in current. Integrating both sides and re-arranging we can get:

Inductors In Series

Inductors In Parallel

So, for 2 inductors in parallel:

Diodes let current flow in one direction, but not the other, and always drop the same voltage across them no matter the src voltage.

Diodes drop the same voltage across them no matter the voltage source rating. So, for example, silicon diode needs about 0.7V to fwd bias, but won't let the voltage drop across it exceed this. So if you don't protect it with a resistor it will allow too much current to flow an potentially overheat!

References

• Diodes and Diode Circuits.
• Accounting for LED resistance, StackExchange.

The total resistance R_A + R_B will determine the time it takes for the transistor to charge, assuming we keep capacitance constant. However, when the capacitor discharges, it only discharges through R_B.

Recall charge time for a cap to charge to 63% of the voltage across is is . So by varying either the resistors or the capacitor the period of the pulse train output on pin 3 can be varied.

The diagrams above and below imagine that there is a switch inside the 555, which there is, its just not a mechanical switch like these diagrams suggest (see later below for more details). As the capacitor charges the voltage across it increases. When it hits 2/3 of the reference voltage, the switch in side the 555 closes such that pin 7 is shorted to ground. The capacitor then immediately starts to discharg through R_B and when the voltage across the capacitor is less than 1/3 the reference voltage the switch opens again, starting the charge cycle and so on.

As the switch also controls the connection between the reference voltage and the output, this produces a pulse train who's frequency is determined by the two resistors and the capacitor, and with a duty cycle that is determined by the two resistors.

The following is a silly little animation of the capacitor discharging through R2. Imagine that the 3 red dots represent the flow of electrons from the negatively charged plate to the positive plate of the capacitor as it discharges. I think normally it would be shown using conventional current flow, but this animation uses actual electron flow. meh.

Wikimedia has a really nice illustration of the components in the 555, which I've copied below and inserted the components outside the chip that we used above to create an astable vibrator. Here, we can see that the switch shown above is really an RS flip flop combined with a transitor.

Each of the components, like the RS flip flop, comparitors and other gates can be further broken down into their transitor/resitor combinations, so the above is just another, slightly more detailed abstraction. The real circuit is far, far more complex when broken down into its "atomic" building blocks!

555 References

• 555 Timer IC - Working Principle, Block Diagram, Circuit Schematics, Dejan, Mechatronics How To.
• NE555 Block Diagram, BlanchardJ / Public domain.
• Sequential Logic Circuits, Electronic Tutorials, SR Flip Flop.
• NAND gate, WikiPedia.

NPN transistors consist of two N-type (negatively doped - excess electroncs) silicon "chunks" sandwiching a P-type (positively doped - exess holes or lacking electrons) as shown below. They are current controlled.

[Ref]

By forward biasing the emitter to base junction with even a small current, the transistor's resistance between the emitter and collector quickly decreses, allowing a relatively large current to from from the emitter to collector. I.e., base current controls current at emitter and collector.

The above configuration is called the common emitter configuration and is probably the most widely used [Ref].

NPN transistors can typically handle up to about 0.8 A. Thus, they are low current devices. For large currents MOSFETs are used (later section).

Saturation region is where the maximum collector current flows and the transistor is basically a closed switch from collector to emitter.

Active mode / region is where there is an almost linear relationship between the terminal currents at the base, collector and emitter. The transistor has some resistance, that is determined by the emitter/base current.

Cut-off region is where the transistor acts like an open switch.

A common NPN transistor is the 2N2222. Looking at the data sheet [Ref] we can find the following properties:

Parameter	Max
Collector-base voltage VCBO	60 V
Collector-emitter voltage VCEO	30 V
Emitter-base voltage VEBO	5 V
Peak collector current	800 mA
Peak base current	200mA
Total power disipation	500 mW

We can see that this device can handle a maximum of 0.8A though its emitter-collector and only 0.2A at the base. It is however, able to tolerate relatively high voltages, just not high currents, which as we said above, you'd need MOSFETs, or even relays for.

Lets represent the above common emitter example as a circuit diagram:

• The base is responsible for initiating transistor action. When a voltage is applied at the base, it gets biased and draws small current which is then used to control large current at the collector and emitter side.
• The base action is considered as an ON-OFF valve which generates current when a proper bias voltage is applied at this terminal.
• The small change at the voltage applied at the base terminal shows a large impact at the output terminals. Actually, base acts as an input and collector acts as an output in NPN transistor.
• In case of silicon transistor emitter-base junction draws voltage around 0.7 when there is no voltage at the base terminal, in order to initiate the electron action and put the transistor in running condition, the base voltage must be greater than 0.7 voltage in case of silicon transistor and 0.3 in case of germanium transistor.

References