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AS Physics 9702 unit 3: Electric Charge

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UNIT 3 – ELECTRIC CHARGE

ELECTRIC CIRCUITS:

For the current to exist it must have a complete path of conductors. This complete path of conductors

is called electric circuit. For example copper wires, which are conductors, are used to connect lamps

in a circuit to complete the path for the flow of charges. The battery is also attached to the circuit to

push these charges around. To draw on a paper the diagram of complete path of charges is called

circuit diagram. It contains symbols for every component of the circuit. Following are some common

circuit symbols:

There are two different ways of connecting circuit components in a circuit to the same battery. They

are called series and parallel circuits. We will discuss about these circuits later in this section.

ELECTRIC CHARGE:

All matter is made up of atoms. Atoms have three elementary particles that are electrons, protons and

neutrons. Since the atom and its particles are very small for us to observe we can understand the

presence of these atomic particles by rubbing two polythene rods (an insulator) with woolen cloth.

These rods when brought close to each other they repel. It means that rods have acquired an electric

charge. There are two types of charges - the positive charge and negative charge. The positive charge

is carried by protons or positive ions and negative charge is carried by electrons or negative ions.

Following table will describe how different substances behave when rubbed with different materials.

Charging an object by rubbing is called electrostatic induction by rubbing or by friction.

Material Rubbed with Charge acquired Behaviour

Polythene rod Woollen cloth Negative Attract each other

Perspex Woollen cloth Positive

Ebonite Fur Negative Attract each other

Glass Silk positive

It must be noted that the charges are not created by rubbing action. When polythene rod is rubbed

with a woolen cloth, some of the electrons of the surface atoms of the cloth transferred to the rod and

therefore the polythene rod become negatively charged and cloth becomes positively charge. That

means that the charges are transferred from cloth to polythene and total charge is always conserved

or same.

The unit of charge is coulomb or C (capital C). The most common letters used to express charges are

Q, q or e. Small ‘e’ is specifically used for expressing the charge of elementary particle electron (e-)

or proton (e+).

Prepared by Faisal Jaffer, revised on Jan 2012

ELECTRIC FIELD:

1. It is a field of electric force.

2. An electric field is a space or region around a charged object Q where a

stationary positive charge qo experience electric force.

3. It is a vector quantity and its direction is along the direction where the

positive charge would move. This means that the electric field is always

out from positive charge and in to negative charge.

4. The electric field is represented by the radial straight lines around the

charge object. Stronger the field more the number of lines.

Electric field intensity or electric field strength

of an ‘E’ electric charge

1. The electric field intensity is defined as force per unit charge. In

equation form this is represented as:

2. The unit of electric field intensity is newton per coulomb or N/C.

3. The electric field around charge Q, is considered to be a uniform

radial field. This means that a charge qo experiences same force

around a charge object Q if it is at equal distance from the centre of

the charge at any position.

4. We can plot a graph of electric field intensity E against the distance r

from its centre. We can see that the graph shows inverse square law

curve that is E inversely proportional to r2.

5. When two charged plates are placed together, the radial fields of the

charges combine to make a uniform electric field. Notice that the

field bulges at the ends; generally we ignore this. In this case we can

show that the electric field intensity is given by a simpler

relationship:

6. E – electric field intensity; V – potential difference between

the two plates and; d - distance between the two plates in

meters. In this case the unit of electric field intensity is

volts/metre V/m which is same as the other unit that is

newton/coulomb N/C.

7. When a charged particle is moving in between the two

parallel plates that are carrying opposite charges and

have uniform electric field between the plates then the

charge particle experience a constant force centripetal

perpendicular to the motion of the particle. The

deflection of the particle will be towards the opposite

charge plate as show in the diagram.


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Exercise no 3.1: Solve the following questions from past paper.

1. Oct/Nov 2010, Paper 12, questions 28, 29

2. May/Jun 2010, Paper 12, questions 26, 27, 28

3. Oct/Nov 2009, Paper 12, questions 26, 27, 28

4. May/Jun 2009, Paper 1, questions 27, 28, 29

5. May/Jun 2008, Paper 1, questions 30, 31,



ELELCTIC CURRENT (I):

Current (I) is defined as the rate of flow of electric charges (Q) in

an electric circuit.

The unit of current is ampere (A). Multiple units of ampere are:

milli-ampere (mA) = 10-3

A and micro-ampere (μA) = 10-6

A

Current is measured by a device called ammeter or multimeter. There are two

types of ammeters; analogue and digital.

Electric charge (Q) in a conductor is carried by atomic particles – electrons or

negative ions. Unit of electric charge is coulomb (C). The quantity of electric

charge of electron or proton is 1.6×10-19

C.

One coulomb is defined as:

a charge passing through any point in a circuit when a steady current of

1 ampere maintained for 1 second, that is:

1coulomb (C) = 1ampere (A)×1second (t).

Conventional current:

The electric current is really a flow of electrons from negative to positive terminal of the battery.

However when it was first discovered, scientists wrongly guessed that something that carries charges

flows from positive to negative terminal and therefore they describe it as conventional current.

Whenever we study electric current and flow of charges we always consider conventional current that

is from positive to negative.

Direct and alternating currents (d.c. and a.c.):

The electrons constantly flowing around the circuit, from the negative

terminal of the battery to the positive terminal, produce direct current

(d.c). All batteries produce direct current.

In mains electricity at homes, the electrons in the circuit move

backwards and forwards 50 to 60 times in one second. This kind of

current is called alternating current (a.c.). The main advantage of using

alternating current over direct current is it can be transmitted from

power stations to our homes at very high voltage which reduces the

amount energy that is lost during the transmission.

Movement of charges in liquids:

Electrolysis:

Electrolysis is the process in which chemical changes are occur in a conducting

liquid when electric charges are passing through it.

The conducting liquid is called electrolyte. The word electrolysis means the

process of breaking molecules of conducting liquid into its parts (ions) by using

electric current. Positive and negative poles of an electric source, such as a

battery, can absorb opposite ions of an electrolyte, causing separation of ions and

creation of a new substance. Liquid metals are not electrolyte since they can pass

current without there being any associated chemical change or making of ions

for example in mercury which is liquid. However solution of sodium chloride

(NaCl) in water is a good example of electrolyte. Some substances that do not

conduct electricity is called non-electrolyte for example sugar-solution.


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The figure illustrates a simple arrangement of producing electrolysis. The plates by which the current

enters and leaves are called electrodes. Electrode connected to the positive terminal of the battery is

called anode and an electrode connected to the negative terminal is called cathode. Consider the

example of sodium chloride (NaCl) in water as an electrolyte. It contains Na+ and Cl

- ions which are

free to move in water and it conduct electric current. Solid sodium chloride cannot conduct electricity

because ions are not free to move but when the current exists through the solution, NaCl splits into

Na+ and Cl

- ions. Sodium ion (Na

+) gains an electron at the cathode and deposit on the surface of the

plate and similarly Chlorine ion (Cl-) losses an electron at anode and deposit on the surface of anode.

Movement of charges in solids:

Metals:

The atomic structures of metals are such that each atom on

average has one outer electron which is not required for

bonding and which need not to remain attached with its atom.

This electron is called free electron or de-localized electron.

When the current does not exist these free electrons move

randomly in all direction throughout the conductor. When the

battery is attached and potential difference is put across the

conductor, it produces an electric field and affects the flow of

free electrons. It pushes the free electrons towards the positive

end of the battery. Thus this creates the flow of charges across

the conductor which means electric current.

Exercise no 3.2: Solve the following questions from past papers.

1. Oct/Nov 2009, Paper 12, question 33




SERIES AND PARALLEL CIRCUITS:

Series Circuit:

A series circuit is a circuit in which components (eg

resistors) are arranged in a chain, so the charges have only

one path to follow.

The current (rate of flow of charges) is same through each

component in series circuit.

The total resistance of the circuit is found by simply adding

up the resistance values of the individual resistors. Equivalent resistance (R) in series circuit

can be expressed by.

where R1 and R2 are the resistances of each resistor.

In series circuit the total potential difference (battery voltage) is the sum of individual

potential differences (p.d.) across each resistor. That is

V = V1 + V2 + ... where V1 and V2 are p.d. across the component R1 and R2.

The current (I) is same in each resistance therefore the ammeter is connected in series with

the other resistances.

In series circuit if one component breaks down then the whole circuit will stop working.

More the resistance of the component, the higher the potential difference across it.

In series circuit the voltage across each resistor divides according to the ratio of resistance

value of each resistor.

Parallel Circuit:

A parallel circuit is a circuit in which the components are

arranged such that each component is directly connected to

the battery. The parallel circuit makes branches for the

current.

The current in a parallel circuit breaks up with some current

flowing along each parallel branch and re-combining when

the branches meet again.

The voltage across each resistor in parallel circuit is same.

Lesser the resistance in the branch more the current in that

branch.

Equivalent resistance of each component or resistors R1 and

R2 in parallel circuit can be expressed by:

or

In parallel circuit the total current is the sum of individual currents in each branch.

I = I1 + I2 + …

Voltage remains same across each resistor that is it has same value as the voltage of the

battery.

The combine resistance of all resistors in parallel circuit is less than the least resistor in the

circuit.

http://physi.files.wordpress.com/2010/02/series_circuit.jpg

http://physi.files.wordpress.com/2010/02/parallel_circuit.jpg


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POTENTIAL DIFFERENCE:

An electric potential difference (V) must exist for current to flow

in an electric circuit.

It is the work done per unit charge as the charge is moved

between two points in an electric circuit.

The potential difference (p.d.) between two points in a circuit is

1V if 1J of electrical energy (E) is transferred to another form of

energy (i.e. to chargers) when 1 coulomb (C) of charge (Q)

passes from one point to another.

or

Replacing the from the definition of charge and current.

The equation will be

or

Measuring potential difference:

A voltmeter is used to measure the electric potential difference

between two points in an electric circuit. It is connected in parallel

across a resistor in the circuit. It has a very high internal resistance.

The unit of potential difference or voltage is volts.

OHMS LAW:

As the potential difference (V) is increased across a given material

(ohmic material or metal) in a circuit, the current (I) flow through the

material also increases.

or

The potential difference (V) between any two points in a conductor is

directly proportional to the current (I) through it if the temperature,

resistance of the conductor and other conditions are constant.

where R is the resistance of a conductor.

RESISTANCE:

The opposition of to the current in a conductor is called resistance of that conductor.

All metals are good conductor of electricity. The best conductor is silver (%) and copper (%) is

next to it. All substance have some degree of resistance, there is no substance possible without

any resistance and normal temperature.

Substances that do not carry current is called insulator. Germanium and silicon have conductivity

in between conductors and insulators. They are called semiconductor.


The unit of resistance is ohm (Greek symbol omega ). One ohm is the resistance when current

of one ampere and potential difference of one volt is applied across the resistor.

A resistance of a cylinder or wire of certain material:

increases if its length (L) increases,

increases if its cross-section area (A) decreases,

depends upon the type of material → ρ

where is the resistivity of the conductor which is constant for every material.

Measuring resistance:

The resistance (R) of a conductor is measured by ohm-meter.

Alternatively the resistance of a conductor can be found by setting up

the circuit shown in figure and measuring the current (I) and potential

difference (V) applied across it. The resistance of the resistor R can be

found by the formula

. Multiple values of (V) and (I) can be

recorded by changing the resistance of a variable resistor.

By plotting the graph between V and I and finding the gradient of the

line. The gradient is the resistance R.

Electromotive force (e.m.f.):

In energy terms the e.m.f. is defined as:

The energy when converted from any form (chemical or mechanical energy) to electrical energy that

it is used to drive one coulomb charge around the complete circuit. This energy per coulomb is called

electromotive force or e.m.f.

The e.m.f. of a battery is across its terminals when it is not connected to the circuit and it is sometimes

called the terminal potential difference. When the circuit is closed, the voltage across the battery falls,

because the energy and the voltage of the battery are lost across the internal resistance of battery.

To measure e.m.f. or potential difference (p.d.) in a circuit the voltmeter should be connected in

parallel. Voltmeter should always have very high internal resistance.

Internal resistance of a cell:

The p.d. across the terminals of a cell depends on the size of the

current being drawn. If no current is being drawn it means the cell is

not connected with the circuit then the potential difference between

the terminal has its maximum value and know as the electromotive

force (e.m.f.) of the cell. This e.m.f. is solely because of the chemical

reaction occurring inside the cell.

The chemical inside the cell creates a resistance to the current (I).

This resistance is called the internal resistance (r) of the cell. When a

cell is connected across an external circuit (load R) some of the e.m.f. is used to drive current through

the load and rest of the emf drives the same current through the internal resistance. The internal

resistance behave as it is in series with the external resistance of the circuit. The equation for the two

resistance connected in series is


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or

or

where Ir is the p.d. across the internal resistance and V is the potential

difference across the external resistance. From equation when I=0 it

means that the cell is not connected to any external resistance then

V=E the emf of the cell.

Measurement of e.m.f. and internal resistance of a cell:

1. Connect the circuit as shown in the diagram.

2. Record six readings of voltmeter (V) and ammeter (I) of the cell by changing the values of

variable resistance R.

3. The resistance of the voltmeter should be higher than the combine resistances of r and R.

4. Plot the graph between V (on y-axis) and I (on x-axis) and draw the best fit straight line. The

equation of the straight line should be .

5. Compare the straight line equation with the equation of e.m.f. or by rearranging

.

6. Comparing these two equations shows gradient of the line m is

–r and y-intercept c is E, the e.m.f. of the battery.

7. The internal resistance of a typical 1.5V cell is 1Ω if the current

is limited to 0.2A, the terminal PD will range from 1.5V when

I= 0 to 1.3V when I=0.2A.

Maximum power delivered by the cell:

Consider the circuit diagram shown in the figure in which the e.m.f.

of the cell is E, the internal resistance is r and driving current is I

through a load of resistance R. The power delivered by the cell to

resistance R is

but we know that

therefore by replacing

The maximum power dissipated by cell is when R=r. A given

source of e.m.f. delivers maximum amount of power to a load

when the resistance of the load is equal to the internal resistance of

the source.








7. May/June 2008, Paper 1, question 38

8. May/June 2010, Paper 22, question 6(a)

9. May/June 2008, paper 2, question 6



I-V Characteristic of various components:

Metal:

Metal conductors obey ohm’s law, provided their temperature does

not change or we can say that the metal conductors have constant

resistance provided its temperature is constant. The I-V graph

between current (I), on y-axis (dependent variable) and voltage (V)

on x-axis (independent variable) is straight line.

Diode:

In semiconductor diode it allows the current only in one direction

and that is forward bias connection. In diode the current is not proportional to voltage (or PD) applied

because when the PD is reversed, the current is almost zero. This is reverse biased connection.

Filament:

In tungsten filament as the current increases, the temperature also rises and the resistance goes up. So

the current is not proportional to PD. This happens because as the current increases in the filament the

temperature also increases which increase the resistance of the conductor and decrease the flow of

charges in the conductor.


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Thermistor:

A thermistor is a heat sensor (resistor) which changes its resistance with the change of

temperature (heat) around it. Its resistance decreases as the temperature increases which is

reverse to the normal conductor. For example:

Icy water 0°C has high resistance, about 12kΩ.

Room temperature 25°C has medium resistance, about 5kΩ.

Boiling water 100°C has low resistance, about 400Ω.

Thermistor is called input transducer. It means it changes its resistance with

the change in environment. The I-V graph of a thermistor is not a straight

line and therefore it does not obey Ohm’s law. As more current is through

the thermistor the graph gets steeper. The thermistor is a semiconductor and

conducts more electricity when heated. This is because as the temperature

increases the thermistor makes available more free electrons to carry current.

Therefore as the current increases the thermistor get hotter and releasing

more electrons resulting in a reduction in resistance.

LDR (Light Dependent Resistor):

An LDR is a light sensor (resistor) which changes its resistance with the

brightness of light around it. It is made from cadmium sulphide compound (CdS) and its resistance

decreases as the brightness of light falling on the LDR increases.

Darkness: maximum resistance, about 106Ω.

Very bright light: minimum resistance, about 100Ω.

LDR is called input transducer. It means it changes resistance with the change in environment. The I-

V graph is a straight line. When light shines on it releases electrons which increases the number of

electrons to carry the current. Thus, as the light increases the current increases resulting in a reduction

in resistance. In dark however no extra electrons are available so the current experiences a greater

resistance.


ELECTRIC POWER:

Rate of doing work is called power. It is define as

replacing

replacing

Unit of power is watts (W) and larger units are 1 kilowatt (kW) = 1000 W and 1megawatt (MW) =

1000 000 W. The power of electrical appliances can be calculated by multiplying the current (I)

passing through it by the potential difference (V) across it.

Exercise no 3.4:

Solve the quiz on the website

http://www.learnabout-electronics.org/resistors_23.php

Solve the following questions from past papers.



http://www.learnabout-electronics.org/resistors_23.php


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KIRCHHOFF’S LAW:

Kirchhoff’s first law –Junction rule - Conservation of charge:

At junction in a circuit, the total current entering is equal to the total current leaving it.

Mathematically ΣI=0

In figure at junction A current I1 and I2 are approaching and current I3 is leaving therefore.

Kirchhoff’s second law – Loop rule - Conservation of energy:

In any closed loop in a circuit, the sum of the e.m.f. (E) must be equal to the sum of all the IR

products.

Mathematically

ΣE = ΣIR

In the circuit in e.m.f. of V1 is E1 and

e.m.f. of V2 is E2. Considering the loop 1

clockwise then the equation can be written

as

for loop 2 anticlockwise

and for loop 3

Substituting the values and solving the

three equations simultaneously we can find

the values of I1, I2 and I3.

Rules for applying Kirchhoff’s Law:

1. Draw an arrow to show the direction of current in each branch of the circuit. Choose any

direction clockwise or anticlockwise. If you chose the wrong direction then the value of

current will turn out to be negative.

2. Mark each resistor with a plus sign at one end and minus sign at the other end, in a way that is

consistent with the direction of current chosen in step 1. Mark each battery such that the

positive terminal considered as higher potential and negative terminal considered as lower

potential. Conventional current always flow from higher potential to lower potential.

3. While calculating the current through a battery the internal resistance is considered as

separate resistance.

4. Apply first and second rule to the circuit and obtained as many independent equations as

many number of variables.

5. Solve the equations simultaneously for the known variables.







POTENTIAL DIVIDER OR VOLTAGE DIVIDER

A potential (or voltage) divider is combination of two resistors, as shown in the

figure. The output voltage V2 from a potential divider will be a proportion of

the input voltage V1 and is determined by the ratio of the two resistance

values.

In the arrangement of the circuit in the diagram the value of V2, the output

voltage can be determine by the formula:

V1 is the input voltage and R1 and R2 are the resistor in series.

This arrangement is normally used to change voltage across a circuit

component, for example to change the brightness of the lamp, or control the

volume (loudness) in a hi-fi amplifier circuit.

Potential divider and LDR:

Now what happend when one of the resistors is replaced with LDR, the light

dependent resistor.

The resistance of LDR decreases as more light falls on it.

It means that there will be low p.d. across R2 and high p.d. across R1.

If a lamp is connected across R1 then the brightness of the lamp increases when the intensity of

light falling on LDR decreases.

Voltage divider circuit gives an output voltage which changes with illumination of the

surrounding.

Potential divider and thermistor:

We can consider the similar situation by replacing thermistor with the R2 in the

circuit.

The resistance of thermistor decreases as the temperature rises.

They are called negative temperature coefficient, or ntc thermistors. A typical

ntc thermistor is made using semiconductor metal oxide materials.

Semiconductors have resistance properties midway between those of conductors

and insulators.

As the temperature rises, more charge carriers become available and the resistance falls.

If we connect a lamp across the resistance R1, then the brightness of the lamp increases if the

temperature of the surrounding increases.



2. May/June 2008, Paper 1, questions 36, 37




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Comparing the E.M.F.s of two cells:

A potentiometer can be used to compare the e.m.fs of

two cells. Consider the circuit below. A resistance wire

of length one meter is connected with a cell called the

driver cell that will remain unchanged. Connect the cell

X, of known E.M.F., with the circuit and find the null

point on the centre deflection ammeter by bringing in the

sliding contact with the resistance wire. Measure the

length of resistance wire as LX (example 0.70m). Repeat

the same procedure by connecting the battery Y of

unknown EMF in the circuit and find the length of wire as LY (example 0.90m).

The ratio of the two e.m.fs is equal to the ratio of their lengths of resistance wire.

Exercise no 3.7: Solve the following questions past papers.



Comparing Electric and Gravitational Fields

There are many analogies that can be drawn between electric fields and gravitational fields.

Theoretical physicists would go as far as saying that the two are possibly different expression of the

same thing. Let us compare the two:

Feature Electric Field Gravity Field Exert force on Positive or negative charge Mass

Constant of Proportionality

where 0 is the permittivity of

free space. The value of can be

changed by adding a material.

G

The value of G, the universal

gravity constant has the same

value for all media, including a

vacuum.

Relationship with distance r Inversely proportional to r2. Inversely proportional to r

2.

Force Equation or

Nature of force Can be attractive or repulsive and

goes from positive to negative

charge

Always attractive pointing

towards the centre of the earth

Acceleration in uniform field

Relative strength Strong at close range Weak. Can only be felt when the

objects are massive

Range Infinite Infinite

The gravitational attraction between particles in an atom is so small and considered negligible. The

nucleus and its electrons are held together entirely by electrostatic forces, and these are involved in

chemical reactions. Gravity forces hold planets together and hold them in their orbits. Electrostatic

forces over the interplanetary distances can be ignored.


Charge to mass ratio of electron

The mass of an electron is 9.11 x 10-31

kg, and its charge is 1.602 ×10-19

C. These quantities are too

small to directly measure, even if you were somehow able to isolate a single electron in the

laboratory. However, using principles of electromagnetism, indirect measurements of the charge and

the mass of the electron can be accomplished. These indirect measurements will be accomplished by

taking advantage of quantities that are directly measurable in the laboratory setting. These direct

quantities will be derived from knowledge of the velocity of an electron moving in a magnetic field.

Consider an electron of charge e is passing in between the two parallel plates of potential difference

V. The direction of electric field is perpendicular to the direction of motion of electron. Electron

creates a curved (trajectory path) attracting towards the positive plate. The electric potential energy

lost by electron is

The kinetic energy gain by the electron at any particular instance is given by

As the electron is accelerating in the electric field it loses its electric potential energy and gains the

kinetic energy (a similar analogy as an object is falling towards the earth in gravitational field).

Equate the two energies.

Rearranging the equation

V the p.d. across the two plates can be recorded from the battery voltage and speed of the electron can

be calculated from the distance travelled by the electron in between the two plates (that is length of

the plates) and time taken. The charge to mass ratio e/m is also called the specific charge of electron.

Electron-volt:

It is the energy required to accelerate an electron through a potential difference of one volt.

Replacing the quantity of charge as e = 1.6×10-19

C and potential difference as 1 volt in equation

This implies that 1ev=1.6×10-19

joules

It is a convenient energy unit, particularly for atomic and nuclear processes. It is the energy given to

an electron by accelerating it through 1 volt of electric potential difference.

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