DC Circuit Theory

The fundamental relationship between voltage, current and resistance in an electrical or electronic circuit is called Ohm’s Law.

  

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 (that is they are Neutral), 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 happy and 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.

Now 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.

Then 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.

Then 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“, although Energy, E lowercase “e” is sometimes used to indicate a generated emf (electromotive force). Then 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 with 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. While A.C. (alternating current) voltage sources are available for domestic house and 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.

Voltage Symbols

A simple relationship can be made between a tank of water and a voltage supply. The higher the water tank above the outlet the greater the pressure of the water as more energy is released, the higher the voltage the greater the potential energy as more electrons are released.

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.

Then Conventional Current Flow gives the flow of electrical current from positive to negative and which is the opposite in direction to the actual flow of electrons.

Electron Flow

The flow of electrons around the circuit is opposite to the direction of the conventional current flow being negative to positive.The actual current flowing in an electrical circuit is composed of electrons that flow from the negative pole of the battery (the cathode) and return back to the positive pole (the anode) of the battery.

This is because the charge on an electron is negative by definition and so is attracted to the positive terminal. This flow of electrons is called Electron Current Flow. Therefore, electrons actually flow around a circuit from the negative terminal to the positive.

Both conventional current flow and electron flow are used by many textbooks. In fact, it makes no difference which way the current is flowing around the circuit as long as the direction is used consistently. The direction of current flow does not affect what the current does within the circuit. Generally it is much easier to understand the conventional current flow – positive to negative.

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 around the circuit.

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.. Whether 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.

Also, as alternating currents (and voltages) are periodic and vary with time the “effective” or “RMS”, (Root Mean Squared) value given as Irms produces the same average power loss equivalent to a DC current Iaverage . 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.

Using the tank of water relationship, current is the equivalent of the flow of water through the pipe with the flow being the same throughout the pipe. The faster the flow of water the greater the current. Note that current cannot exist without voltage so any current source whether DC or AC likes a short or semi-short circuit condition but hates any open circuit condition as this prevents it from flowing.

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, but never negative. 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 absorbed 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 ) 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.

In other words the ease by which current flows. 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 spelt 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

Hopefully by now you should have some idea of how electrical Voltage, Current and Resistance are closely related together. 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 electrical 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

Magnetism & Electromagnetism

Magnetism

One of the fundamental properties of matter is magnetism. Magnetism is related to electricity. In fact, the fundamental cause of all magnetism effects is due to the movements of electric charges. Common materials for magnets are iron, steel, cobalt and nickel. They are suitable to make magnets due to their atomic structures.

• An atom consists of a central, positively charged nucleus surrounded by negatively charged electrons. A common view of the electrons is that they orbit around the central nucleus, while spinning on their axes. This view is not exactly correct, but its alright at this level. Due to the charge on the electrons, the movements of these electrons will give rise to magnetic effects. These magnetic effects can be seen as tiny atomic magnets.
• The tiny magnetic effects occurs in all substances. Then, why aren’t all substances magnetic? This is due to their atomic structures. In those materials, the electrons are arranged in configurations that result in the magnetic effects cancelling out one another.
• Once those tiny atomic magnets are aligned properly, it will give rise to a strong combined magnetic effect. At this point, the substance is considered to be magnetised and is a proper magnet.
• Lodestone is the only natural substance that behaves as a magnet. Magnetic materials like steel and iron can be made into magnets.

Properties of magnets

Since  magnetism is related to the movements of electrons. It is not surprising that the basic ideas of magnetism is very similar to those of electrostatics.

• All the magnets have two types of poles: north-seeking poles or north poles and south-seeking poles or south poles.
• The magnetic strength is the strongest at the poles of the magnet.
• When you freely suspend a bar magnet in a horizontal position, the magnetic field of the bar magnet will interact with the magnetic field of the Earth. This will cause the bar magnet to come to rest in a north-south direction, where the north pole of the magnet points to the north pole of the Earth.
• Like poles repel and unlike poles attract. (just as like charges repel and unlike charges attract).
• Magnets attract magnetic materials such as iron, steel, cobalt and nickel.
• The stronger a magnet, the larger will be the attractive or repulsive force between other magnets.
• The closer together the two magnets are, the greater is the magnetic force between them.

Note:

• All magnets have a north and south poles – 2 poles. Cutting a bar magnet in half simply produces two smaller magnets, each with its own north and south poles. What if you cut the half-bar-magnet? You will just obtain two smaller magnets, each with its own north and south poles. There is currently no experimental nor theoretical evidence for the existence of a magnet containing only 1 pole (magnetic monopole). If a magnetic monopole is found, most of the Physics texts will have to be rewritten.
• Only magnets can be made to repel each other. Otherwise, the magnets will attract all other magnetic materials.
• The Earth has a giant magnet, its axis is oriented more or less in the direction of the Earth’s rotation. The North pole of the Earth is actually the south pole of the Earth’s magnet. (The magnetic poles actually does not align perfectly with the real north and south pole. There is a small deviation. But let’s not concern ourselves with this for now.)

Magnetic materials are matter that is attracted by magnets.

• Magnetic materials can be made into magnets.

e.g. Iron, steel, nickel, cobalt and many alloys based on these metals.

Non-magnetic materials are matter that is not attracted by magnets.

• Non-magnetic materials cannot be made into magnets.

e.g. Wood, glass, plastics and metals such as copper and brass.

Note: It would be good if you can remember the examples.

induced Magnetism & Electrical Method Of Magnetisation

Magnetic Induction is one of the ways making magnetic materials like steel and iron into magnets. In other words, magnetic induction is a process of inducing magnetism in an ordinary piece of magnetic material.

• This method involves simply placing the magnetic material (soft iron) close to a strong magnet without touching.
• The soft iron bar becomes an induced magnet with the end nearer the magnet having opposite polarity to that of the magnet.
• Hence, the soft iron bar is attracted and attached to the permanent magnet. Magnetic induction process reveals how magnetic materials can be attracted to magnets.
• Induced magnetism is a temporary process. If the permanent magnet is removed, the magnetic material will usually lose its induced magnetism.

Electrical method for magnetisation

For magnetization, a direct current flowing into a solenoid (a long insulated wire coiled into a cylinder) produces a magnetic field that, inside the coil, is uniform in strength and direction.

• The solenoid becomes a magnet.

A steel bar placed inside the coil for a short while becomes magnetised due to magnetic induction from the solenoid.

• The polarities of the magnet depend on the direction of current flow.

Magnetisation by electric current method creates more powerful magnets than other magnetization methods such as stroking.

Magnetic Field And Magnetic Field Lines

Magnetic Field is the region around a magnet where other magnetic material will experience a force.

A magnetic field can be graphically represented by magnetic field lines which indicates its strength and direction.

Note: Magnetic field is a vector quantity! (It has both magnitude AND direction!)

• When the field lines are close together at a point, the point is said to have a strong magnetic field.
• Arrows in the field lines outside the magnets show the direction in which a free north pole would move (from north pole to south pole).
• Field lines NEVER cross over.
• Compass is used to find the direction and pattern of magnetic field. It has a permanent magnet needle which is free to rotate in a horizontal plane. The north pole of compass magnet (arrow head) will align and point along the magnetic field line direction.

IMPORTANT: Please note that for the last two diagrams, the field lines are NOT pushing against one another. Do NOT be tempted to say that the like poles repel because the field lines push against one another. It is NOT correct!

Interesting tidbits:

Magnetic field strength can be measured using a teslameter.

Plotting of magnetic field lines with a compass

Apparatus Needed: Bar magnet, plotting paper and plotting compass.

Procedure:

1. Place the bar magnet at the centre of the piece of paper so that its north pole is aligned as shown.
2. Place the compass near one pole of the magnet, and mark the positions of the ends N and S, of the compass needle by pencil dots. Then, move the compass until  the end of the compass is over the second dot, and mark the new position of the other with a third dot.
3. Repeat the above until reaching the other pole. Join the series of dots and this will give a field line of the magnetic field. Use this method to plot other field lines on both sides of this magnet.

temporary and permanent magnets

Iron as a temporary magnet:

• Iron can be easily magnetised or demagnetised (soft magnetic material. It can even be magnetized by a weak magnetic field. it is therefore suitable to be used in temporary magnets.
• When mixed with other metals (e.g. Ni, Cu, Mn, Si), powerful temporary magnets can be made.
• These temporary magnets are used to make temporary electromagnets. Electromagnets lose its magnetism when it is removed from magnetising fields. Electromagnets are very useful because they can be turned on and off and their strengths can be varied.
• In order to shield or contain any magnetic effects, soft permeable iron is also used as effective magnetic shields. (magnetic keepers)

E.g. Electromagnets can be used for such tasks as moving cars or sorting metals from other landfill materials. Other applications are in circuit breakers, magnetic relays, electric bells, audio and video tapes transformers etc.

Steel as a permanent magnet

• Compared to iron, steel cannot be easily magnetised or demagnetised (hard magnetic material). It can only be magnetized by a strong magnetic field. But, steel has the ability to retain its magnetism once it is magnetized. This trait allows steel to be suitable to be used in permanent magnets.
• Steel is typically mixed with other magnetic material to ensure structural stability. In this way, strong permanent magnets are made.

E.g. Permanent magnets are used in compasses, magnetic door catches, moving coil galvanometers, d.c. motors, a.c. generators, loudspeakers, and for many other purposes.

Note: Theoretical limit for a permanent magnetic field is 5 Tesla. Electromagnets made with ordinary wires can produce steady fields of 34 Tesla.

Magnetic field due to current in a straight wire

Movement of electric charge is an underlying cause of magnetism. Hence, an electric current, being a flow of charge, produces a magnetic field. If the current is flowing in a wire, the shape of the magnetic field is dependent on the configuration of the wire.

The magnetic field lines produced by a current in a straight wire are in the form of circles with the wire as its centre.

Right-hand rule can be used to find the direction of the magnetic field produced due to current flow.

• Right-hand rule: Grasp the wire with right hand so that the thumb points in the direction of the conventional current, then the wrapped fingers will encircle the wire in the direction of the magnetic field.

The magnetic field is strong in the region around the wire and weakens with increasing distance, i.e., the field lines near the wire are drawn closer to another. With increasing distances, concentric circles are further apart.

The larger the current, the stronger is the magnetic field.

Magnetic field due to current in a solenoid

 

Solenoid consists of a length of insulated wire coiled into a cylinder shape.

• Current in solenoid produces a stronger magnetic field inside the solenoid than outside. The field lines in this region are parallel and closely spaced showing the field is highly uniform in strength and direction.
• Field lines outside the solenoid are similar to that of a bar magnet, and it behaves in a similar way – as if it had a north pole at one end and south pole at the other end. Strength of the field diminishes with distance from the solenoid.
• Strength of the magnetic field can be increased by:
  1. increasing the current in the coil
  2. increasing the number of coils in the solenoid; and
  3. using a soft iron core within the solenoid.
• Reversing the direction of the current reverses the direction of the magnetic field.

Right-hand rule can be used to find the direction of the magnetic field. In this case, point the wrapped fingers (along the coil) in the direction of the conventional current. Then, the thumb will point to the direction of magnetic field within the solenoid.

Electric bell

The well-known application of electromagnet is the electric bell.

• When the ‘push’ switch is depressed, the circuit is closed. Current passes through the electromagnet windings and the core becomes magnetised.
• The magnetised core attracts the iron armature which makes the striker hits the gong.
• However, the movement of the armature opens the ‘make and break’ switch which switches the electromagnet off. The iron armature springs back to its original position, closing the ‘make and break’ switch and start the cycle again.

Notes:

• Soft iron is used to make electromagnets as it gains and loses magnetism quickly depending on existence of magnetic fields. The armature is also made of soft iron which can induce magnetism rapidly.
• No matter what direction is the current flow, the bell rings continuously as long as the ‘push’ switch is closed because any pole induces the armature.

Circuit breaker

An excess current circuit breaker is a ‘trip’ switch opened by an electromagnet in the same circuit when the current through the windings exceeds a certain value.

Unlike a ‘make and break’ switch, a ‘trip’ is designed to stay open after it has been opened by the electromagnet. The trip switch is reset manually after the cause of the excessive current has been removed.

Force on current-carrying conductor

When current-carrying conductor is placed in a magnetic field, it will experience a force when the magnetic field direction is not parallel to the current direction. The magnitude of the force is maximum when the magnetic field and current directions are mutually perpendicular to each other. The force decreases when the angle between the magnetic field and current directions is smaller than 

90∘${90}^{\circ }$.

Factors that affect the strength of the force:

• Angle between the magnetic field and current directions (More about this below)
• Magnetic field strength (Stronger magnetic field →$\to$ stronger force)
• Amount of current in conductor (Higher current →$\to$ stronger force)
• Length of conductor within magnetic field (Longer conductor →$\to$ stronger force)

If the current direction is PARALLEL to the magnetic field, there will NO force on the conductor by the magnetic field. The magnitude of the force is MAXIMUM when the angle between the magnetic field and current direction is 90∘${90}^{\circ }$.

This is commonly exploited to produce a turning effect in a current-carrying coil to produce an electric motor.

It does not have to be a current carrying conductor to experience a force due to the magnetic field. The magnetic field actually interacts with the moving electrons in the conductor to produce the force. Hence, electrons that are moving in the direction perpendicular to the magnetic field will experience the force as well. This means that if you pass an electron beam through a magnetic field, it will be deflected. (provided it is perpendicular)