Basic Electronics on the Go - Norton’s Theorem

From http://www.electronics-tutorials.ws/dccircuits/dcp_8.html

Nortons Theorem states that “Any linear circuit containing several energy sources and resistances can be replaced by a single Constant Current generator in parallel with a Single Resistor“.

As far as the load resistance, R_L is concerned this single resistance, R_S is the value of the resistance looking back into the network with all the current sources open circuited and I_S is the short circuit current at the output terminals as shown below.

The value of this “constant current” is one which would flow if the two output terminals where shorted together while the source resistance would be measured looking back into the terminals, (the same as Thevenin).
For example, consider our now familiar circuit from the previous section

To find the Nortons equivalent of the above circuit we firstly have to remove the centre 40Ω load resistor and short out the terminals A and B to give us the following circuit.

When the terminals A and B are shorted together the two resistors are connected in parallel across their two respective voltage sources and the currents flowing through each resistor as well as the total short circuit current can now be calculated as (done with Mesh Current Analysis, it seems):

If we short-out the two voltage sources and open circuit terminals A and B, the two resistors are now effectively connected together in parallel. The value of the internal resistor Rs is found by calculating the total resistance at the terminals A and B giving us the following circuit.

Find the Equivalent Resistance (Rs)

 

Having found both the short circuit current, Is and equivalent internal resistance, Rs this then gives us the following Nortons equivalent circuit.

Nortons equivalent circuit.

 

 We now have to solve with the original 40Ω load resistor connected across terminals A and B as shown below.

Again, the two resistors are connected in parallel across the terminals A and B which gives us a total resistance of:

The voltage across the terminals A and B with the load resistor connected is given as:

Then the current flowing in the 40Ω load resistor can be found as:

Nortons Theorem Summary

The basic procedure for solving a circuit using Nortons Theorem is as follows:

• 1. Remove the load resistor R_L or component concerned.
• 2. Find R_S by shorting all voltage sources or by open circuiting all the current sources.
• 3. Find I_S by placing a shorting link on the output terminals A and B.
• 4. Find the current flowing through the load resistor R_L.

In a circuit, power supplied to the load is at its maximum when the load resistance is equal to the source resistance. In the next tutorial we will look at Maximum Power Transfer. The application of the maximum power transfer theorem can be applied to either simple and complicated linear circuits having a variable load and is used to find the load resistance that leads to transfer of maximum power to the load.

Basic Electronics on the Go - Thevenin’s Theorem

From http://www.electronics-tutorials.ws/dccircuits/dcp_7.html

In this tutorial we will look at one of the more common circuit analysis theorems (next to Kirchhoff´s) that has been developed, Thevenin’s Theorem.

Thevenin’s Theorem states that “Any linear circuit containing several voltages and resistances can be replaced by just one single voltage in series with a single resistance connected across the load“. In other words, it is possible to simplify any electrical circuit, no matter how complex, to an equivalent two-terminal circuit with just a single constant voltage source in series with a resistance (or impedance) connected to a load as shown below.

Thevenin’s equivalent circuit.

  

Consider the circuit from the previous section.

 

Firstly, to analyse the circuit we have to remove the centre 40Ω load resistor connected across the terminals A-B, and remove any internal resistance associated with the voltage source(s). This is done by shorting out all the voltage sources connected to the circuit, that is v = 0, or open circuit any connected current sources making i = 0. The reason for this is that we want to have an ideal voltage source or an ideal current source for the circuit analysis.

The value of the equivalent resistance, Rs is found by calculating the total resistance looking back from the terminals A and B with all the voltage sources shorted. We then get the following circuit.

Find the Equivalent Resistance (Rs)

 

 

The voltage Vs is defined as the total voltage across the terminals A and B when there is an open circuit between them. That is without the load resistor R_L connected.

We now need to reconnect the two voltages back into the circuit, and as V_S  =  V_AB the current flowing around the loop is calculated as:

This current of 0.33 amperes (330mA) is common to both resistors so the voltage drop across the 20Ω resistor or the 10Ω resistor can be calculated as:

V_AB  =  20  –  (20Ω x 0.33amps)  =   13.33 volts.

or

V_AB  =  10  +  (10Ω x 0.33amps)  =   13.33 volts, the same.

Then the Thevenin’s Equivalent circuit would consist or a series resistance of 6.67Ω’s and a voltage source of 13.33v. With the 40Ω resistor connected back into the circuit we get:

and from this the current flowing around the circuit is given as:

which again, is the same value of 0.286 amps, we found using Kirchoff´s circuit law in the previous circuit analysis tutorial.

Thevenin’s theorem can be used as another type of circuit analysis method and is particularly useful in the analysis of complicated circuits consisting of one or more voltage or current source and resistors that are arranged in the usual parallel and series connections.

While Thevenin’s circuit theorem can be described mathematically in terms of current and voltage, it is not as powerful as Mesh or Nodal analysis in larger networks because the use of Mesh or Nodal analysis is usually necessary in any Thevenin exercise, so it might as well be used from the start. However, Thevenin’s equivalent circuits of Transistors, Voltage Sources such as batteries etc, are very useful in circuit design.

Thevenin’s Theorem Summary

The basic procedure for solving a circuit using Thevenin’s Theorem is as follows:

• 1. Remove the load resistor R_L or component concerned.
• 2. Find R_S by shorting all voltage sources or by open circuiting all the current sources.
• 3. Find V_S by the usual circuit analysis methods.
• 4. Find the current flowing through the load resistor R_L.

In the next tutorial we will look at Nortons Theorem which allows a network consisting of linear resistors and sources to be represented by an equivalent circuit with a single current source in parallel with a single source resistance.

Basic Electronics on the Go - Nodal Voltage Analysis

From http://www.electronics-tutorials.ws/dccircuits/dcp_6.html

Nodal Voltage Analysis complements the previous mesh analysis in that it is equally powerful and based on the same concepts of matrix analysis.  Nodal Voltage Analysis uses the “Nodal” equations of Kirchhoff’s first law to find the voltage potentials around the circuit.
So by adding together all these nodal voltages the net result will be equal to zero. Then, if there are “n” nodes in the circuit there will be “n-1” independent nodal equations and these alone are sufficient to describe and hence solve the circuit.
At each node point write down Kirchhoff’s first law equation, that is: “the currents entering a node are exactly equal in value to the currents leaving the node” then express each current in terms of the voltage across the branch. For “n” nodes, one node will be used as the reference node and all the other voltages will be referenced or measured with respect to this common node.

Nodal Voltage Analysis Circuit

 

In the above circuit, node D is chosen as the reference node and the other three nodes are assumed to have voltages, Va, Vb and  Vc with respect to node D. For example;

 

 As Va = 10v and Vc = 20v , Vb can be easily found by:

In the next tutorial we will look at Thevenins Theorem which allows a network consisting of linear resistors and sources to be represented by an equivalent circuit with a single voltage source and a series resistance.

Basic Electronics on the Go - Mesh Current Analysis

From http://www.electronics-tutorials.ws/dccircuits/dcp_5.html

 While Kirchhoff´s Laws give us the basic method for analysing any complex electrical circuit, there are different ways of improving upon this method by using Mesh Current Analysis or Nodal Voltage Analysis that results in a lessening of the math’s involved and when large networks are involved this reduction in maths can be a big advantage.

 For example, consider the electrical circuit example from the previous section.

Mesh Current Analysis Circuit

An easier method of solving the above circuit is by using Mesh Current Analysis or Loop Analysis which is also sometimes called Maxwell´s Circulating Currents method. Instead of labelling the branch currents we need to label each “closed loop” with a circulating current.
As a general rule of thumb, only label inside loops in a clockwise direction with circulating currents as the aim is to cover all the elements of the circuit at least once. Any required branch current may be found from the appropriate loop or mesh currents as before using Kirchhoff´s method.

For example: :    i₁ = I₁ , i₂ = -I₂  and  I₃ = I₁ – I₂

We now write Kirchhoff’s voltage law equation in the same way as before to solve them but the advantage of this method is that it ensures that the information obtained from the circuit equations is the minimum required to solve the circuit as the information is more general and can easily be put into a matrix form.

For example, consider the circuit from the previous section.

 First we need to understand that when dealing with matrices, for the division of two matrices it is the same as multiplying one matrix by the inverse of the other as shown.

having found the inverse of R, as V/R is the same as V x R^-1, we can now use it to find the two circulating currents.

Mesh Current Analysis Summary.

The basic procedure for solving Mesh Current Analysis equations is as follows:

• 1. Label all the internal loops with circulating currents. (I₁, I₂, …I_L etc)
• 2. Write the [ L x 1 ] column matrix [ V ] giving the sum of all voltage sources in each loop.
• 3. Write the [ L x L ] matrix, [ R ] for all the resistances in the circuit as follows;
• •   R₁₁ = the total resistance in the first loop.
  •   R_nn = the total resistance in the Nth loop.
  •   R_JK = the resistance which directly joins loop J to Loop K.
• 4. Write the matrix or vector equation [V]  =  [R] x [I] where [I] is the list of currents to be found.

As well as using Mesh Current Analysis, we can also use node analysis to calculate the voltages around the loops, again reducing the amount of mathematics required using just Kirchoff’s laws.

Basic Electronics on the Go - Kirchhoffs Circuit Law

From http://www.electronics-tutorials.ws/dccircuits/dcp_4.html

Gustav Kirchhoff’s Current Law is one of the fundamental laws used for circuit analysis. His current law states that for a parallel path the total current entering a circuits junction is exactly equal to the total current leaving the same junction.


In other words the algebraic sum of ALL the currents entering and leaving a junction must be equal to zero as: Σ IIN = Σ IOUT.


This idea by Kirchhoff is commonly known as the Conservation of Charge, as the current is conserved around the junction with no loss of current.



Here, the 3 currents entering the node, I₁, I₂, I₃ are all positive in value and the 2 currents leaving the node, I₄ and I₅ are negative in value. Then this means we can also rewrite the equation as;

I₁ + I₂ + I₃ – I₄ – I₅ = 0

 The term Node in an electrical circuit generally refers to a connection or junction of two or more current carrying paths or elements such as cables and components. Also for current to flow either in or out of a node a closed circuit path must exist.

Kirchhoffs Second Law – The Voltage Law, (KVL)

Kirchhoffs Voltage Law or KVL, states that “in any closed loop network, the total voltage around the loop is equal to the sum of all the voltage drops within the same loop” which is also equal to zero. In other words the algebraic sum of all voltages within the loop must be equal to zero.

Kirchhoffs Voltage Law

 

 

  Starting at any point in the loop continue in the same direction noting the direction of all the voltage drops, either positive or negative, and returning back to the same starting point. It is important to maintain the same direction either clockwise or anti-clockwise or the final voltage sum will not be equal to zero. 

Common DC Circuit Theory Terms:

• • Circuit – a circuit is a closed loop conducting path in which an electrical current flows.
• • Path – a single line of connecting elements or sources.
• • Node – a node is a junction, connection or terminal within a circuit were two or more circuit elements are connected or joined together giving a connection point between two or more branches. A node is indicated by a dot.
• • Branch – a branch is a single or group of components such as resistors or a source which are connected between two nodes.
• • Loop – a loop is a simple closed path in a circuit in which no circuit element or node is encountered more than once.
• • Mesh – a mesh is a single open loop that does not have a closed path. There are no components inside a mesh.

A Typical DC Circuit

 

Kirchhoffs Circuit Law Example No1

Find the current flowing in the 40Ω Resistor, R₃

 

The circuit has 3 branches, 2 nodes (A and B) and 2 independent loops.

Using Kirchhoffs Current Law, KCL the equations are given as;

At node A :    I₁ + I₂ = I₃

At node B :    I₃ = I₁ + I₂

Using Kirchhoffs Voltage Law, KVL the equations are given as;

Loop 1 is given as :    10 = R₁ I₁ + R₃ I₃ = 10I₁ + 40I₃

Loop 2 is given as :    20 = R₂ I₂ + R₃ I₃ = 20I₂ + 40I₃

Loop 3 is given as :    10 – 20 = 10I₁ – 20I₂

As I₃ is the sum of I₁ + I₂ we can rewrite the equations as;

Eq. No 1 :    10 = 10I₁ + 40(I₁ + I₂)  =  50I₁ + 40I₂

Eq. No 2 :    20 = 20I₂ + 40(I₁ + I₂)  =  40I₁ + 60I₂

We now have two “Simultaneous Equations” that can be reduced to give us the values of I₁ and I₂ 

Substitution of I₁ in terms of I₂ gives us the value of I₁ as -0.143 Amps

Substitution of I₂ in terms of I₁ gives us the value of I₂ as +0.429 Amps

As :    I₃ = I₁ + I₂

The current flowing in resistor R₃ is given as :    -0.143 + 0.429 = 0.286 Amps

and the voltage across the resistor R₃ is given as :    0.286 x 40 = 11.44 volts

The negative sign for I₁ means that the direction of current flow initially chosen was wrong, but never the less still valid. In fact, the 20v battery is charging the 10v battery.

Application of Kirchhoffs Circuit Laws

These two laws enable the Currents and Voltages in a circuit to be found, ie, the circuit is said to be “Analysed”, and the basic procedure for using Kirchhoff’s Circuit Laws is as follows:

• 1. Assume all voltages and resistances are given. ( If not label them V1, V2,… R1, R2, etc. )
• 2. Label each branch with a branch current. ( I1, I2, I3 etc. )
• 3. Find Kirchhoff’s first law equations for each node.
• 4. Find Kirchhoff’s second law equations for each of the independent loops of the circuit.
• 5. Use Linear simultaneous equations as required to find the unknown currents.

  We can also use loop analysis to calculate the currents in each independent loop which helps to reduce the amount of mathematics required by using just Kirchhoff's laws. In the next tutorial about DC circuits, we will look at Mesh Current Analysis to do just that.

(to be updated)

Basic Electronics on the Go - Electrical Units of Measure

From http://www.electronics-tutorials.ws/dccircuits/dcp_3.html

 The following table gives a list of some of the standard electrical units of measure used in electrical formulas and component values.

Standard Electrical Units

 

Electrical Parameter

Measuring Unit

Symbol

Description

Voltage

Volt

V or E

Unit of Electrical Potential V = I × R

Current

Ampere

I or i

Unit of Electrical Current I = V ÷ R

Resistance

Ohm

R or Ω

Unit of DC Resistance R = V ÷ I

Conductance

Siemen

G or ℧

Reciprocal of Resistance G = 1 ÷ R

Capacitance

Farad

C

Unit of Capacitance C = Q ÷ V

Charge

Coulomb

Q

Unit of Electrical Charge Q = C × V

Inductance

Henry

L or H

Unit of Inductance VL = -L(di/dt)

Power

Watts

W

Unit of Power P = V × I  or  I2 × R

Impedance

Ohm

Z

Unit of AC Resistance Z2 = R2 + X2

Frequency

Hertz

Hz

Unit of Frequency ƒ = 1 ÷ T

 

Multiples and Sub-multiples

There is a huge range of values encountered in electrical and electronic engineering between a maximum value and a minimum value of a standard electrical unit. For example, resistance can be lower than 0.01Ω’s or higher than 1,000,000Ω’s. By using multiples and submultiple’s of the standard unit we can avoid having to write too many zero’s to define the position of the decimal point. The table below gives their names and abbreviations.

Prefix	Symbol	Multiplier	Power of Ten
Terra	T	1,000,000,000,000	1012
Giga	G	1,000,000,000	109
Mega	M	1,000,000	106
kilo	k	1,000	103
none	none	1	100
centi	c	1/100	10-2
milli	m	1/1,000	10-3
micro	µ	1/1,000,000	10-6
nano	n	1/1,000,000,000	10-9
pico	p	1/1,000,000,000,000	10-12

 

So to display the units or multiples of units for either Resistance, Current or Voltage we would use as an example:

• 1kV = 1 kilo-volt  –  which is equal to 1,000 Volts.
• 1mA = 1 milli-amp  –  which is equal to one thousandths (1/1000) of an Ampere.

As well as the “Standard” electrical units of measure shown above, other units are also used in electrical engineering to denote other values and quantities such as:

• •  Wh – The Watt-Hour, The amount of electrical energy consumed by a circuit over a period of time. Eg, a light bulb consumes one hundred watts of electrical power for one hour. It is commonly used in the form of: Wh (watt-hours), kWh (Kilowatt-hour) which is 1,000 watt-hours or MWh (Megawatt-hour) which is 1,000,000 watt-hours.
• •  dB – The Decibel, The decibel is a one tenth unit of the Bel (symbol B) and is used to represent gain either in voltage, current or power. It is a logarithmic unit expressed in dB and is commonly used to represent the ratio of input to output in amplifier, audio circuits or loudspeaker systems.
  For example, the dB ratio of an input voltage (Vin) to an output voltage (Vout) is expressed as 20log₁₀ (Vout/Vin). The value in dB can be either positive (20dB) representing gain or negative (-20dB) representing loss with unity, ie input = output expressed as 0dB.
• •  ω – Angular Frequency, Another unit which is mainly used in a.c. circuits to represent the Phasor Relationship between two or more waveforms is called Angular Frequency, symbol ω. This is a rotational unit of angular frequency 2πƒ with units in radians per second, rads/s. The complete revolution of one cycle is 360 degrees or 2π, therefore, half a revolution is given as 180 degrees or π rad.
• •  τ – Time Constant, The Time Constant of an impedance circuit or linear first-order system is the time it takes for the output to reach 63.7% of its maximum or minimum output value when subjected to a Step Response input. It is a measure of reaction time.

Basic Electronics on the Go - Ohms Law and Power

 From http://www.electronics-tutorials.ws/dccircuits/dcp_2.html

 Georg Ohm found that, at a constant temperature, the electrical current flowing through a fixed linear resistance is directly proportional to the voltage applied across it, and also inversely proportional to the resistance. This relationship between the Voltage, Current and Resistance forms the basis of Ohms Law and is shown below.

Any Electrical device or component that obeys “Ohms Law” that is, the current flowing through it is proportional to the voltage across it ( I α V ), such as resistors or cables, are said to be “Ohmic” in nature, and devices that do not, such as transistors or diodes, are said to be “Non-ohmic” devices.

Electrical Power in Circuits

Electrical Power, ( P ) in a circuit is the rate at which energy is absorbed or produced within a circuit. A source of energy such as a voltage will produce or deliver power while the connected load absorbs it. Light bulbs and heaters for example, absorb electrical power and convert it into either heat, or light, or both. The higher their value or rating in watts the more electrical power they are likely to consume.
The quantity symbol for power is P and is the product of voltage multiplied by the current with the unit of measurement being the Watt ( W ). Prefixes are used to denote the various multiples or sub-multiples of a watt, such as: milliwatts (mW = 10^-3W) or kilowatts (kW = 10³W).
Then by using Ohm’s law and substituting for the values of V, I and R the formula for electrical power can be found as:

To find the Power (P)

[ P = V x I ]      P (watts) = V (volts) x I (amps)

Also,

[ P = V² ÷ R ]      P (watts) = V² (volts) ÷ R (Ω)

Also,

[ P = I² x R ]      P (watts) = I² (amps) x R (Ω)

Electrical Power Rating

Electrical components are given a “power rating” in watts that indicates the maximum rate at which the component converts the electrical power into other forms of energy such as heat, light or motion. For example, a 1/4W resistor, a 100W light bulb etc.
Electrical devices convert one form of power into another. So for example, an electrical motor will covert electrical energy into a mechanical force, while an electrical generator converts mechanical force into electrical energy. A light bulb converts electrical energy into both light and heat.

Electrical Energy in Circuits

 Electrical Energy is the capacity to do work, and the unit of work or energy is the joule ( J ). Electrical energy is the product of power multiplied by the length of time it was consumed. Electrical power can be defined as the rate of doing work or the transferring of energy.

The maths involved when dealing with joules, kilojoules or megajoules to express electrical energy, can end up with some big numbers and lots of zero’s, so it is much more easier to express electrical energy consumed in Kilowatt-hours.

Kilowatt-hours are the standard units of energy used by the electricity meter in our homes to calculate the amount of electrical energy we use and therefore how much we pay.

Basic Electronics on the Go - DC Circuits - DC Circuit Theory

From http://www.electronics-tutorials.ws/dccircuits/dcp_1.html



All materials are made up from atoms, and all atoms consist of protons, neutrons and electrons. Protons, have a positive electrical charge. Neutrons have no electrical charge while Electrons, have a negative electrical charge. Atoms are bound together by powerful forces of attraction existing between the atoms nucleus and the electrons in its outer shell.


When these protons, neutrons and electrons are together within the atom they are stable. But if we separate them from each other they want to reform and start to exert a potential of attraction called a potential difference.
If we create a closed circuit these loose electrons will start to move and drift back to the protons due to their attraction creating a flow of electrons. This flow of electrons is called an electrical current.
  The electrons do not flow freely through the circuit as the material they move through creates a restriction to the electron flow. This restriction is called resistance.

  All basic electrical or electronic circuits consist of three separate but very much related electrical quantities called: Voltage, ( v ), Current, ( i ) and Resistance, ( Ω ).

Electrical Voltage

Voltage, ( V ) is the potential energy of an electrical supply stored in the form of an electrical charge. Voltage can be thought of as the force that pushes electrons through a conductor and the greater the voltage the greater is its ability to “push” the electrons through a given circuit. As energy has the ability to do work, this potential energy can be described as the work required in joules to move electrons in the form of an electrical current around a circuit from one point or node to another.

 The difference in voltage between any two points, connections or junctions (called nodes) in a circuit is known as the Potential Difference, ( p.d. ) commonly called the Voltage Drop. The Potential difference between two points is measured in Volts with the circuit symbol V, or lowercase “v“.  The greater the voltage, the greater is the pressure (or pushing force) and the greater is the capacity to do work.

A constant voltage source is called a DC Voltage while a voltage that varies periodically with time is called an AC voltage. Voltage is measured in volts, with one volt being defined as the electrical pressure required to force an electrical current of one ampere through a resistance of one Ohm. Voltages are generally expressed in Volts with prefixes used to denote sub-multiples of the voltage such as microvolts ( μV = 10^-6 V ), millivolts ( mV = 10^-3 V ) or kilovolts ( kV = 10³ V ). Voltage can be either positive or negative.

 Batteries or power supplies are mostly used to produce a steady D.C. (direct current) voltage source such as 5v, 12v, 24v etc in electronic circuits and systems. A.C. (alternating current) voltage sources are for domestic houses, industrial power and lighting as well as power transmission. The mains voltage supply in the United Kingdom is currently 230 volts a.c. and 110 volts a.c. in the USA.

 General electronic circuits operate on low voltage DC battery supplies of between 1.5V and 24V dc The circuit symbol for a constant voltage source usually given as a battery symbol with a positive, + and negative, – sign indicating the direction of the polarity. The circuit symbol for an alternating voltage source is a circle with a sine wave inside.

Electronic circuits operate on  DC battery supplies of between 1.5V and 24V dc. The circuit symbol for a constant voltage source is  usually given as a battery symbol with a positive, + and negative, – sign indicating the direction of the polarity. The circuit symbol for an alternating voltage source is a circle with a sine wave inside.

Voltage Symbols

 

 Voltage is always measured as the difference between any two points in a circuit and the voltage between these two points is generally referred to as the “Voltage drop“. Note that voltage can exist across a circuit without current, but current cannot exist without voltage and as such any voltage source whether DC or AC likes an open or semi-open circuit condition but hates any short circuit condition as this can destroy it.

Electrical Current

Electrical Current, ( I ) is the movement or flow of electrical charge and is measured in Amperes, symbol i, for intensity). It is the continuous and uniform flow (called a drift) of electrons (the negative particles of an atom) around a circuit that are being “pushed” by the voltage source. In reality, electrons flow from the negative (-ve) terminal to the positive (+ve) terminal of the supply and for ease of circuit understanding conventional current flow assumes that the current flows from the positive to the negative terminal.

Generally in circuit diagrams the flow of current through the circuit usually has an arrow associated with the symbol, I, or lowercase i to indicate the actual direction of the current flow. However, this arrow usually indicates the direction of conventional current flow and not necessarily the direction of the actual flow.

Conventional Current Flow

 

Conventionally this is the flow of positive charge around a circuit, being positive to negative. The diagram at the left shows the movement of the positive charge (holes) around a closed circuit flowing from the positive terminal of the battery, through the circuit and returns to the negative terminal of the battery. This flow of current from positive to negative is generally known as conventional current flow.

 This was the convention chosen during the discovery of electricity in which the direction of electric current was thought to flow in a circuit. To continue with this line of thought, in all circuit diagrams and schematics, the arrows shown on symbols for components such as diodes and transistors point in the direction of conventional current flow.

In electronic circuits, a current source is a circuit element that provides a specified amount of current for example, 1A, 5A 10 Amps etc, with the circuit symbol for a constant current source given as a circle with an arrow inside indicating its direction.

Current is measured in Amps and an amp or ampere is defined as the number of electrons or charge (Q in Coulombs) passing a certain point in the circuit in one second, (t in Seconds).
Electrical current is generally expressed in Amps with prefixes used to denote micro amps ( μA = 10^-6A ) or milliamps ( mA = 10^-3A ). Note that electrical current can be either positive in value or negative in value depending upon its direction of flow.

 Current that flows in a single direction is called Direct Current, or D.C. and current that alternates back and forth through the circuit is known as Alternating Current, or A.C..  AC or DC current only flows through a circuit when a voltage source is connected to it with its “flow” being limited to both the resistance of the circuit and the voltage source pushing it.

 Even though alternating currents (and voltages) are periodic and vary with time the “effective” or “RMS”, (Root Mean Squared) value given as I_rms produces the same average power loss equivalent to a DC current I_average. Current sources are the opposite to voltage sources in that they like short or closed circuit conditions but hate open circuit conditions as no current will flow.

Resistance

Resistance, ( R ) is the capacity of a material to resist or prevent the flow of current or, more specifically, the flow of electric charge within a circuit. The circuit element which does this perfectly is called the “Resistor”.

 Resistance is a circuit element measured in Ohms, Greek symbol ( Ω, Omega ) with prefixes used to denote Kilo-ohms ( kΩ = 10³Ω ) and Mega-ohms ( MΩ = 10⁶Ω ). Note that resistance cannot be negative in value only positive.

Resistor Symbols

 

The amount of resistance a resistor has is determined by the relationship of the current through it to the voltage across it which determines whether the circuit element is a “good conductor” – low resistance, or a “bad conductor” – high resistance. Low resistance, for example 1Ω or less implies that the circuit is a good conductor made from materials such as copper, aluminium or carbon while a high resistance, 1MΩ or more implies the circuit is a bad conductor made from insulating materials such as glass, porcelain or plastic.
A “semiconductor” on the other hand such as silicon or germanium, is a material whose resistance is half way between that of a good conductor and a good insulator. Hence the name “semi-conductor”. Semiconductors are used to make Diodes and Transistors etc.
Resistance can be linear or non-linear in nature. Linear resistance obeys Ohm’s Law as the voltage across the resistor is linearly proportional to the current through it. Non-linear resistance, does not obey Ohm’s Law but has a voltage drop across it that is proportional to some power of the current.
Resistance is pure and is not affected by frequency with the AC impedance of a resistance being equal to its DC resistance and as a result can not be negative. Remember that resistance is always positive, and never negative.
A resistor is classed as a passive circuit element and as such cannot deliver power or store energy. Instead resistors absorb power that appears as heat and light. Power in a resistance is always positive regardless of voltage polarity and current direction.
For very low values of resistance, for example milli-ohms, ( mΩ´s ) it is sometimes much easier to use the reciprocal of resistance ( 1/R ) rather than resistance ( R ) itself. The reciprocal of resistance is called Conductance, symbol ( G ) and represents the ability of a conductor or device to conduct electricity.
 High values of conductance implies a good conductor such as copper while low values of conductance implies a bad conductor such as wood. The standard unit of measurement given for conductance is the Siemen, symbol (S).
The unit used for conductance is mho (ohm spelled backward), which is symbolized by an inverted Ohm sign ℧. Power can also be expressed using conductance as: p = i²/G = v²G.

 The relationship between Voltage, ( v ) and Current, ( i ) in a circuit of constant Resistance, ( R ) would produce a straight line i-v relationship with slope equal to the value of the resistance as shown.

Voltage, Current and Resistance Summary

 The relationship between Voltage, Current and Resistance forms the basis of Ohm’s law. In a linear circuit of fixed resistance, if we increase the voltage, the current goes up, and similarly, if we decrease the voltage, the current goes down. This means that if the voltage is high the current is high, and if the voltage is low the current is low.

 

Likewise, if we increase the resistance, the current goes down for a given voltage and if we decrease the resistance the current goes up. Which means that if resistance is high current is low and if resistance is low current is high.

Then we can see that current flow around a circuit is directly proportional ( ∝ ) to voltage, ( V↑ causes I↑ ) but inversely proportional ( 1/∝ ) to resistance as, ( R↑ causes I↓ ).

A basic summary of the three units is given below.

• Voltage or potential difference is the measure of potential energy between two points in a circuit and is commonly referred to as its ” volt drop “.
• When a voltage source is connected to a closed loop circuit the voltage will produce a current flowing around the circuit.
• In DC voltage sources the symbols +ve (positive) and -ve (negative) are used to denote the polarity of the voltage supply.
• Voltage is measured in ” Volts ” and has the symbol ” V ” for voltage or ” E ” for energy.
• Current flow is a combination of electron flow and hole flow through a circuit.
• Current is the continuous and uniform flow of charge around the circuit and is measured in ” Amperes ” or ” Amps ” and has the symbol ” I “.
• Current is Directly Proportional to Voltage ( I ∝ V )
• The effective (rms) value of an alternating current has the same average power loss equivalent to a direct current flowing through a resistive element.
• Resistance is the opposition to current flowing around a circuit.
• Low values of resistance implies a conductor and high values of resistance implies an insulator.
• Current is Inversely Proportional to Resistance ( I 1/∝ R )
• Resistance is measured in ” Ohms ” and has the Greek symbol ” Ω ” or the letter ” R “.

Quantity	Symbol	Unit of Measure	Abbreviation
Voltage	V or E	Volt	V
Current	I	Ampere	A
Resistance	R	Ohms	Ω