The graph below shows how the current from an AC supply varies with time. Here are some of the terms used to describe AC. Note the similarities with those used for circular motion and SHM.
Above, a magnet is moved into a coil. If the flux through the coil changes (at a steady rate) by DF in time Dt, then an EMF of is induced in each turn. But there are N turns in series. So, the total induced EMF E is as follows:
For example, if the flux changes by 6 Wb in 2 s, and the coil has 100 turns, then the total induced EMF is 300 V.
21.1 Magnetic field B
Magnetic Field B is a field of force that exist around the magnetic body or current carrying conductor.
Magnetic field B, also known as magnetic flux density or magnetic field Intensity.
we can summarize the result with the following equation:
21.2 Force on a moving charge
Unit bagi magnetic flux density adalah Tesla,T atau Wbm-2
To find out the direction of the force also can be shown using Fleming’s left-hand rules.
Satu eletron bergerak dalam medan magnet. Pada satu ketika laju elektron ialah 3.0 ´ 106 ms-1. Magnitud daya magnet yang bertindak pada elektron ialah 5.0 ´ 1013 N. Sudut di antara arah halaju elektron dan arah daya magnet ialah 30°. Kira ketumpatan fluks magnet pada kedudukan elektron medan itu.
[cas elektron = -1.6 ´ 10-19 C]
21.3 Force on a current-carrying conductor
Above, a current-carrying wire is at right-angles to a uniform magnetic field. The field exerts a force on the wire. The direction of the force is given by Fleming’s left-hand rule . The size of the force depends on the current I, the length l in the field, and the strength of the field. This effect can be used to define the magnetic field strength, known as the magnetic flux density, B:
FB = BIl (1)
B is a vector. The SI unit of B is the testa (T). For example, if the magnetic flux density is 2 T, then the force on 2 m of wire carrying a current of 3 A is 2 x 2 x 3 = 12 N.
If a wire is not at right angles to the field, then the above equation becomes
where q is the angle between the field and the wire. As q becomes less, the force becomes less. When the wire is parallel to the field, sin q = 0, so the force is zero.
Satu konduktor lurus panjang 2m membawa arus 1.5A dan di letakkan dalam medan magnet. Medan itu mempunyai ketumpatan fluks magnet bermagnitud 3.0 ´ 10-3 T. Sudut antara arah medan dan konduktor ialah 30°. Kirakan magnitud daya magnet yang bertindak pada konduktor dan nyatakan arah daya itu.
21.4 Magnetic fields due to currents
The Biot-Savart law,
On the top, a short length dl of thin wire, carrying a current I, causes a magnetic flux density dB at P. According to the Biot-Savart law
With a suitable constant, this can be turned into an equation:
For a vacuum (and effectively for air), the value of k is 10-7 T m A-1. However, in practice, another constant, m0, is used, and the above equation is rewritten as follows:
is possible to derive equations for B near wires and inside coils carrying a current I.
B near an infinitely long, thin, straight wire At a distance a from such a wire (as on the top)
Arus sebanyak 10A mengalir melalui seutas dawai mencancang lurus yang panjang. Kirakan komponen mengufuk medan magnet Bumi. Jika terdapat satu titik neutral 8.0cm dari dawai itu. [m0= 4p ´ 10-7 Hm-1]
B at the centre of a thin coil Or the axis of such a coil, of N turns and radius r (as on the top),
Arus yang sama magnitud mengalir secara bergilir-gilir melalui seutas dawai tegak lurus yang panjang dan satu gegelung membulat berjejari 10cm dimana satahnya tegak dan selari dengan komponen mengufuk medan magnet pada titik berjarak 10cm di utara atau di selatan dari dawai itu terhadap paduan medan magnet di pusat gegelung itu.
Satu gegelung membulat diletakkan, dimana satahnya adalah mencancang dan paksinya membuat sudut kecil q dengan meridian magnet itu. Arus dilalukan mengelilingi gegelung supaya medan yang dihasilkan berkecenderungan untuk menentang medan Bumi. Satu magnet mengufuk yang kecil di letakkan di pusat gegelung itu.
Perihalkan dan terangkan kesan ke atas magnet itu apabila kekuatan arus bertambah. Gegelung itu mempunyai jejari min 10cm,50 lilitan dan arus sebanyak 0.5A mengalir didalamnya. Jika q=12° dan magnet mengarah ke Timur-Barat.Kirakan komponen mengufuk medan magnet Bumi.
B inside an infinitely long solenoid (coil) The field inside such a solenoid (as on above) is uniform. If n is the number of turn per unit length (per m), then
This equation is a reasonable approximation for any solenoid which is at least ten times longer than it is wide.
Berapa banyakkah lilitan mesti dipunyai oleh satu solenoid jika panjang solenoid itu 2.0m dan arus 5.0A mengalir melaluinya supaya arus menghasilkan ketumpatan fluks magnet bermagnitud 2.0 ´ 10-2 T di pusat solenoid ?
B inside a solenoid with a core The value of B is changed by a core. For example, with a pure iron core, B is increased by a factor of about 1000 (depending on the temperature). The previous equation then becomes:
B = µrµ0 nI
µr, is called the relative permeability of the material. So, for pure iron, µr, is about 1000.
An electromagnet is a solenoid with a core of high µr.
21.5 Force between two current-carrying conductors
Force between two current-carrying wires
X and Y above are two infinitely long, straight wires in a vacuum. The current in X produces a magnetic field, whose flux density is B at Y. As a result, there is a force on Y. F is the force acting on length l.
From equation (1) FB = BI2 l
• The above equation gives the force of X on Y. Working out the force of Y on X gives exactly the same result.
• If the two currents are in the same direction (as above), then the wires attract each other. If the two currents are in opposite directions, then the wires repel.
Tiga konduktor yang selari, P, Q dan R berada pada satah yang sama.Jarak antara P dan Q adalah 4cm dan antara Q dan R ialah 2 cm. Arus dalam P dan Q adalah 10A dan 5A masing-masing dan mengalir pada arah yang berlawanan.Daya paduan ke atas Q adalah 5 ´ 10-4N per meter dan bertindak ke arah P. Kirakan magnitud dan arah arus dalam R.
21.6 Definition of ampere
Defining the ampere
The SI unit of current is defined as follows:
One ampere is the current which, flowing through two infinitely long, thin, straight wires placed one metre apart in a vacuum, produces a force of 2 x 10-7 newtons on each metre length of wire.
Using the various factors in equation
the above definition can be expressed in the following form (for simplicity, units have been omitted):
If I1=I2=1A,a=1m and l=1m,then F= 2×10-7N. Substituting these in equation above gives µ0 = 4p x 10-7. The above definition is not a practical way of fixing a standard ampere. This is done by measuring the force between two current-carrying coils.
– Measure current by using the principle of the force between two paralell wire using mechanical
m = jisim pemberat W
b = jarak F ke tuas
c = jarak berat ke tuas
L = jarak XY
apabila sistem tuas seimbang kita dapati
FB = BIL
Maka FB = µ0n I . IL
21.7 Torque on a coil
Lets consider the force on PQ and RS that involve in producing the torque.
Force that produce on PQ and RS have the same magnitude but different direction.
L = height of coil(length of the coil in the magnetic field) and N = no. of turns carrying current,I.
q = angle (below the horizontal from the plan view) between magnetic flux density and the coil.
[coil area,A = Lb]
So the equation for torque will be
q = 0°
t = BIAN
21.8 Determination of ratio e/m and q/m
Using an electron gun
Lets consider the electron gun.
Lets consider the movement of electron in an electro gun
1. The kinetic energy gain by electron = Electric potential energy of electron
2. Electron velocity :
3. Electric force, FE = Magnetic Force, FB , when it’s in equilibrium
4. From equation (2) and (3) we can conclude:
Todetermine any positive charge,q/m using spectrometer.
1. any positivly charge velocity,
2. The charges follow the circular path, the centripetal force of the charge.
3.Magnetic force of charges
21.9 Hall effect
1. apabila arus mantap I melalui konduktor/semikonduktor
2. kemudian diletakkan kedalam medan magnet yang kuat dimana I berserenjang dengan B.
3. Medan magnet melencongkan cas positif ke bahagian atas dan cas negatif ke bahagian bawah
4. Pemisahan ini menghasilkan medan elektrik E yang berserenjang dengan arah aliran arus I
– Bila cas bertambah
– Medan elektrik juga bertambah
– Daya gerak elektrik juga meningkat
5. Pemisahan akan berhenti bila daya E, FE=FB
Magnetic force = Electric force
 Oxford Dictionary
 Fajar Bakti STPM V2 m.s 113
15.1 Internal resistance
15.2 Kirchhoff s laws
15.3 Potential divider
15.4 Potentiometer and Wheatstone bridge
Voltage (PD and EMF)
In the circuit below, several cells have been linked in a line to form a battery. The potential difference (PD) across the battery terminals is 12 volts (V). This means that each coulomb (C) of charge will ‘spend’ 12 joules of energy in moving round the circuit from one terminal to the other.
Figure 15- 1
The PD across the bulb is also 12 V. This means that, for each coulomb pushed through it, 12 J of electrical energy is changed into other forms (heat and light energy).
PD may be measured using a voltmeter as shown above.
PD, energy, and charge are linked by this equation:
Energy transformed = charge x PD
For example, if a charge of 2 C moves through a PD of 3 V, the energy transformed is 6 J.
The voltage produced by the chemical reactions inside a battery is called the electromotive force (EMF). When a battery is supplying current, some energy is wasted inside it, which reduces the PD across its terminals. For example, when a torch battery of EMF 3.0 V is supplying current, the PD across its terminals be might be only 2.5 V.
15.1 Internal resistance
(a) explain the effects of internal resistance on the terminal potential difference of a battery in a circuit;
In reality, when a battery is supplying current, its output PD is less than its EMF. The greater the current, the lower the output PD. This reduced voltage is due to energy dissipation in the battery. In effect, the battery has internal resistance. Mathematically, this can be treated as an additional resistor in the circuit.
Figure 15- 2
The battery above is supplying a current I to an external circuit. The battery has a constant internal resistance r.
From Kirchhoff’s second law :
Figure 15- 3
The graph above shows how V varies with I. Unlike earlier graphs, V is on the vertical axis.
• When R is zero, V is zero. In other words, when the battery is in short circuit (its terminals directly connected), its output PD is zero. In this situation, the battery is delivering the maximum possible current, , which is equal to . Also, the battery’s entire energy output is being wasted internally as heat.
Figure 15- 4
15.2 Kirchhoff’s law
(b) state and apply Kirchhoff s laws;
Figure 15- 5
1. Figure 15-5 shows three typical circuit diagrams that might need to be solved (e.g. given the resistances of all the resistors and the voltages of all the batteries, find all of the currents). Figure 15-5 (a) can be solve easily using Ohm’s Law, but (b) and (c) cannot be solved using the same law. Instead, we must write down Kirchhoff’s laws and solve the equations.
Kirchhoff’s first law (KFL)
Figure 15- 6
Junction is a point where two or more conductor meet together.
The currents at junctions X and Y above illustrate a law which applies to all circuits:
Kirchhoff’s first law
The algebraic sum of currents in a network of conductors meeting at a point is zero
It arises because, in a complete circuit, charge is never gained or lost. The junction rule is based on the conservation of the electric charge . So the total rate of flow of charge is constant. This means that :
Figure 15- 7
Used Kirchhoff’s First Law:
Kirchhoff’s second law (KSL)
Energy, work and EMF
1. When we discuss about the KSL we have to represent the EMF in term of magnitude and direction inside the circuit. The EMF device always keeps one of their terminal labeled ‘+’ at higher electric potential than labeled ‘-’. This will present in arrow diagram as:
Figure 15- 8
2. when connected to the circuit, EMF will causes a net flow of positive charge from positive terminal to negative terminal in the same direction as EMF, this flow is part of current. The flows of current through the load (resistor) within the circuit will made the EMF drop this concept name as voltage drop. The direction of the voltage drop oppose the current flow.
Figure 15- 9
Figure 15- 10
The arrangement above is called ‘a circuit’. But, really, there are two complete circuits through the battery. To avoid confusion, these will be called loops.
Figure 15- 11
Loop 1 and Loop 2 can be form
Figure 15- 12
In the circuit above, charge leaves the battery with electrical potential energy. As the charge flows round a loop, its energy is ‘spent’ – in stages – as heat. The principle that the total energy supplied is equal to the total energy spent (conservation of energy) is expressed by Kirchhoff’s second law.
Kirchhoff’s second law
Round any closed loop of a circuit, the algebraic sum of the EMFs is equal to the algebraic sum of the PDs (i.e. the algebraic sum of all the IRs).
This would means that :
•From the law, it follows that if sections of a circuit are in parallel, they have the same PD across them.
•’Algebraic’ implies that the direction of the voltage must be considered. There are two rule have to be followed to determine the direction of the voltage.
EMF rule: for a move through ideal EMF device (loop direction) in the direction of EMF arrow, the EMF is ‘+’ (+E) : in the opposite direction is ‘-‘ (-E)
Resistance rule: for a move through a resistance (loop direction) in the direction of current, the voltage drop is ‘-‘ (-IR)
For example, in the circuit below, it’s assume that the current is flow in counter clock wise, the EMF of the right-hand battery is taken as negative (-4 V) because it is opposing the loop direction and the voltage drop is positive because it’s oppose to the loop direction, therefore:
Figure 15- 13
(a) Algebraic sum of EMFs = 18 + (-4) = +14V
(b) Algebraic sum of IRs (Voltage drop) = (2 x 3W) + (2 x 4W) = +14 V
Applying the second Kirchhoff’s law the equation will be :
Resistors in parallel
Figure 15- 14
From Kirchhoff’s second law (applied to the various loops):
E = IR (Loop with total Resistor)
E = I1 R1 (Loop with Resistor R1)
E = I2 R2 (Loop with Resistor R2)
From Kirchhoff’s first law I = I1 + I2.
Resistors in series
If R1 and R2 below have a total resistance of R then R is the single resistance which could replace them.
Figure 15- 15
From Kirchhoff’s first law, all parts of the circuit have the same current /through them because there is only one input and one output
From Kirchhoff’s second law
E= IR and E= IR1 + IR2.
So IR = IR1 + IR2
For example, if R1 = 3 W and R2 = 6 W, then R = 9 W.
15.3 Potential divider
(c) explain a potential divider as a source of variable voltage;
(d) explain the uses of shunts and multipliers;
a voltage divider (also known as a potential divider) is a linear circuit that produces an output voltage (Vout) that is a fraction of its input voltage (Vin)
A potential divider or potentiometer like the one below passes on a fraction of the PD supplied to it.
Figure 15- 21
In the input loop above, the total resistance = R1 + R2.
But Vout = IR2,
•The above analysis assumes that no external circuit is connected across R2. If such a circuit is connected, then the output PD is reduced.
In electronics, a potential divider can change the signals from a sensor (such as a heat or Iight.detector) into voltage changes which can be processed electrically. For example, if R2 is a thermistor, then a rise in temperature will cause a fall in R2 and therefore a fall in Vout. Similarly, if R2 is a lightdependent resistor (LDR), then a rise in light level will cause a fall in R2, and therefore a fall in Vout.
Potential dividers are not really suitable for high-power applications because of energy dissipation
Shunt and multiplier
(a) Conversion of Galvanometer to ammeter
Figure 15- 22
Shunts is a resistor connected in parallel
(b) Conversion of Galvanometer to voltmeter
Figure 15- 23
15.4 Potentiometer and Wheatstone bridge
(e) Explain the working principles of a potentiometer, and its uses;
(f) Explain the working principles of a Wheatstone bridge, and its uses;
(g) Solve problems involving potentiometer and Wheatstone bridge.
Potentiometer is an instrument that can be used to measure the emf of a source without drawing (considering) any current from the source.
Function : To measure emf a cell
Key Idea : make sure the galvanometer as a null detector
Figure 15- 24
E = lV
V = potential difference per unit length of AB.
L = The length of wire
l = length that galvanometer show zero reading
(a) Measuring a cell’s internal resistance.
Figure 15- 25
Figure 15- 26
If a graph is plotted,
(b) Comparing resistance
Figure 15- 27
1. A Wheatstone bridge is an electrical circuit used to measure an unknown electrical resistance by balancing two legs of a bridge circuit.
2. A bridge circuit is a type of electrical circuit in which two circuit branches (usually in parallel with each other) are "bridged" by a third branch connected between the first two branches at some intermediate point along them:
Figure 15- 28. (a) a parallel circuit , (b) a Bridge circuit
14. Electric Current
14.1 Conduction of electricity
14.2 Drift velocity
14.3 Current density
14.4 Electric conductivity and resistivity
if two materials are rubbed together, electrons may be transferred from one to another. As a result, one gains negative charge, while the other is left with an equal positive charge. If the materials are insulators, the transferred charge does not readily flow away. It is sometimes called static electricity.
Figure 14- 1
A charged object will attract an uncharged one. The charged rod has extra electrons. Being uncharged, the foil has equal amounts of – and + charge. The – charges are repelled by the rod and tend to move away, while the + charges are attracted. However, the force of attraction is greater because of the shorter distance.
Figure 14- 2
Charge which collects in one region because of the presence of charge on another object is called induced charge.
14.1 Conduction of electricity
(b) explain the mechanism of conduction of electricity in metals;
Figure 14- 3
In the circuit above, chemical reactions in the cell push electrons out of the negative (-) terminal, round the circuit, to the positive (+) terminal. This flow of electrons is called a current.
An arrow in the circuit indicates the direction from the + terminal round to the -. Called the conventional direction, it is the opposite direction to the actual electron flow.
The SI unit of current is the ampere (A).
A current of 1 A is equivalent to a flow of 6 x 1018 electrons per second. However, the ampere is not defined in this way, but in terms of its magnetic effect .
\ One Ampere is the current which, flowing through two infinitely long, thin, straight wires placed one metre apart in a vacuum, produces a force of 2´10-7 N on each metre length of wire
Current may be measured using an ammeter as above.
Conductors and insulators
Current flows easily through metals and carbon. These materials are good conductors because they have free electrons which can drift between their atoms.
Most non-metals are insulators. They do not conduct because all their electrons are tightly held to atoms and not easily moved. Although liquids and gases are usually insulators, they do conduct if they contain ions.
Semiconductors, such as silicon and germanium, are insulators when cold but conductors when warm.
What happen inside the conductor?
Charge can be calculated using this equation:
Charge,Q = current,I x time,t
The SI unit of charge is the coulomb (C).
Case in point
if a current of 1 A flows for 1 s, the charge passing is 1 C. (This is how the coulomb is defined.) Similarly, if a current of 2 A flows for 3 s, the charge passing is 6 C.
Energy and electrical power
Figure 14- 4
Above, charge Q passes through a resistor in time t. Work W is done by the charge, so energy W is transformed – the electrons lose electrical potential energy and the lattice gains internal energy (it heats up).
W, Q, and V are linked by this equation:
But Q= It,
so W= VIt (1)
Applying V = IR to the above equation gives
For example, if a current of 2 A flows through a 3 W resistor for 5 s, W = 22 x 3 x 5 = 60 J. So the energy dissipated is 60 J. Double the current gives four times the energy dissipation.
• Equation (1) can be used to calculate the total energy transformation whenever electrical potential energy is changed into other forms (e.g. KE and internal energy in an electric motor). Equations (2) are only valid where all the energy is changed into internal energy. Similar comments apply to the power equations which follow.
14.2 Drift velocity
(c) explain the concept of drift velocity;
Current and drift velocity
1. we can express current in terms of the drift velocity of the moving charges.
Most electrons are bound to their atoms. However, in a metal, some are free electrons which can move between atoms. When a PD is applied, and a current flows, the free electrons are the charge carriers.
Figure 14- 5
in the wire above, free electrons (each of charge e) are moving with an average speed v. n is the number density of free electrons: the number per unit volume (per m3).
14.3 Current Density
(e) define electric current density and conductivity;
• The number density of free electrons is different for different metals. For copper, it is 8 x 1028 m-1.
• When liquids conduct, ions are the charge carriers. The above equations apply, except that e and n must be replaced by the charge and number density of the ions.
14.4 Electrical conductivity and resistivity
(j) explain the dependence of resistivity on temperature for metals and semiconductors by
(k) discuss the effects of temperature change on the resistivity of conductors, semiconductors and superconductors.
If a PD V is applied across a conductor, and a current I flows, then V = IR.
However, as V is the cause of the current and I s the effect, it is more logical to write this as:
Figure 14- 6
The resistance R of a conductor depends on its length l and cross-sectional area A:
With this equation, the resistance of a wire can be calculated if its dimensions and resistivity are known.
14.6 Dependence of resistance on temperature
1. Current Density
2. Electrical Conductivity
3. Electrical resistivity
so electrical Conductivity
Resistance and temperature
A conducting solid is made up of a lattice of atoms. When a current flows, electrons move through this lattice.
Figure 14- 8
Metals : when free electrons drift through a metal, they make occasional collisions- with the lattice. These collisions are inelastic and transfer energy to the lattice as internal energy. That is why a metal has resistance. If the temperature of a metal rises, the atoms of the lattice vibrate more vigorously. Free electrons collide with the lattice more frequently, which increases the resistance.
Semiconductors (e.g. silicon) At low temperature, the electrons are tightly bound to their atoms. But as the temperature rises, more and more electrons break free and can take part in conduction. This easily outweighs the effects of more vigorous lattice vibrations, so the resistance decreases. At around 100-150 °C, breakdown occurs. There is a sudden fall in resistance – and a huge increase in current. That is why semiconductor devices are easily damaged if they start to overheat.
The conduction properties of a semiconductor can be changed by doping it with tiny amounts of impurities. For example, a diode can be made by doping a piece of silicon so that a current in one direction increases its resistance while a current in the opposite direction decreases it.
The graphs above are for a typical metal conductor and one type of thermistor. The thermistor contains semiconducting materials