ocr physics notes

8/13/2019 OCR Physics Notes

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Particles and RadiationConstituents of the Atom

The constituents of the atom are protons, neutrons and electrons . The protons andneutrons (nucleons) are found in the nucleus of atoms. The nucleus of an atom is

surrounded by empty space in which there are electrons.

Proton, Neutron & Electron Data

Atoms & Isotopes

Atoms are described by their proton number (Z), which is the number of protons they

contain. And their nucleon number (A), which is the number of nucleons their nucleus

contains (nucleon number = number of protons + number of neutrons). For example theelement X below has a proton number of Z and a nucleon number of A.
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Example; uranium- 235 has 92 protons so its proton number is 92. Ithas 92 protons plus 143 neutrons in its nucleus so its nucleon number is 235.

Isotopes are atoms which have the same number of protons but different numbers of

neutrons. Isotopes are all atoms of the same element. We can see below that uranium-238

still has 92 protons but it now has 146 neutrons so its nucleon number is now 238.

Specific charge

If you divide the charge (Q) of a particle or atom by its mass (m) then you will have found

the specific charge in coulombs per kilogram (C kg -1).

Q1) what is the specific charge of a proton at rest.
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Stable and Unstable Nuclei

There are four fundamental forces;

gravity electromagnetic force strong nuclear force weak nuclear force

The protons in a nucleus are all positively charged and so they repel each other (this is the

electromagnetic force in action). This should push the protons apart but it doesnt so there

must be another force which keeps the nucleus together. This force is called the STRONG

NUCLEAR FORCE.

The strong nuclear force

The strong nuclear force holds neutrons and protons (nucleons) together in the nucleus.

Hadrons (mesons & baryons) experience the strong nuclear force but leptons do not.

The strong nuclear force acts over a very short range. It can be both attractive & repulsive.

It gives rise to short range attraction between adjacent nucleons, up to a distance of

about 3 x 10 -15m . (or 3 femtometers). It also gives rise to very short range repulsion below 0.5 x 10 -15m (or 0.5 femtometers).

Stable & Unstable Nuclei

Bismuth with a proton number (z) of 83 is the stable nuclei with the highest number of

protons. All nuclei with proton numbers above 83 are unstable, they are RADIOACTIVE.

The radioactive elements emit;

alpha particles (a) - 2 protons and 2 neutrons (helium nucleus) beta particles (b) a high speed electron gamma rays (g) a photon

Alpha decay (a)

The radioactive parent nuclide decays into a new lighter daughter nuclide by emitting and

alpha particle.

Example; the parent nuclide thorium-232 decays into the daughter nuclide radium-228.


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The proton and nucleon numbers on each side of the decay equation must balance. So if X

decays into Y. The nucleon number of Y must be 4 less than X, and the proton number of Ymust be 2 less than X.

Beta decay (b -)

A beta -particle is produced when a neutron in the parent nuclide decays into a proton by

emitting a beta - particle and an antineutrino .

Example; carbon-14 decaying into nitrogen-14

When the parent decays into the nucleus the nucleon number stays the same BUT the

proton number is one less in Y then it was in Z.

Neutrino

An antineutrino is emitted in the above decay, this is the antiparticle of the neutrino. These

particles have no charge and nearly zero mass.

Gamma Radiation (g)

When nuclide emits a photon of electromagnetic radiation it is called a gamma (g) ray.
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Particles, Antiparticles & Photons

Every type of particle has a corresponding antiparticle, for example;

the positron is the antiparticle of the electron the antiproton is the antiparticle of the proton the antineutron is the antiparticle of the neutron the antineutrino is the antiparticle of the neutrino

The positron for example has the same mass as an electron but it has a positive (+) charge

whereas and electron has a negative (-) charge.

Pair production and annihilation

When a particle and its antiparticle meet each other they annihilate each other. Their mass

is converted into energy in the form of photons .

This is an example of mass being converted into energy but it can also work the other way

around with energy being converted into mass.

High energy photons can produce a particle and its antiparticle, this is called pair

production .

Example; A gamma photon with enough energy can produce an electron and a positron.
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Photons

Electromagnetic radiation (like gamma rays, x-rays and visible light etc.) have wave

properties and they can also behave as particles, these particles are called photons.

The energy (E) of a photon depends on its frequency (f).

E = energy of the photon in joules, J h = the Plank constant 6.63 x 10 -34Js f = frequency in hertz, Hz c = speed of light 3.00 x 10 8 metres per second, ms -1 l = wavelength in metres, m
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Particle Interactions

There are four fundamental forces;

gravity electromagnetic force strong nuclear force weak nuclear force

To explain the forces between particles we use the concept of exchange particles or

bosons .

Gravity gravitons

All particles with mass attract each other with the force of gravity , the mechanism by whichparticles attract each other is through the exchange of particles called gravitons (as yet

undetected).

Electromagnetic force virtual photons

The virtual photon is the exchange particle (or boson) which carries the electromagnetic

force between charged particles. Particles with electric charges can either attract or repel

each other by exchanging particles called virtual photons.

Strong nuclear force gluons

Gluons are the exchange particles involved in the strong nuclear force interaction.

Weak nuclear force W+, W- bosons

W and Z bosons ( in A-level we just need the W + and W - bosons) are the exchange particles

involved in the weak nuclear force interaction.

The weak force acts within the nucleus, quarks and leptons excerpt forces on each other byexchanging bosons. The weak nuclear force is very weak and acts over a very small distance.

Feynman diagrams

Feynman diagrams are visual representations of particle interactions which also show the

exchange particles involved.


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Repulsion between electrons (e -)

Above two electrons exchange a photon (g) as they repel each other.

A proton (p) and an electron (e -) combine to form a neutron (n) and a neutrino (n).

The exchange particle in the above interaction is a W+

boson.
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Classification of Particles

The most basic way of classifying particles is by their mass.

Hadrons are the heaviest particles. This group is then spilt up into baryons and mesons .Baryons are the heaviest particles of all, followed by mesons.

Leptons are the lightest particles.

Hadrons

Hadrons are subject to the strong nuclear force, they are not fundamental particles as they

are made up of quarks.

Baryons , the proton is the only stable baryon all other baryons eventually decay into aproton. All baryons contain three quarks. See the examples below. proton neutron

Antibaryons, see the examples below antiproton antineutron

Mesons, all mesons contain a quark and an antiquark. See the examples below.

pion kaon

Leptons

Leptons , are subject to the weak nuclear force (they do not feel the strong nuclear force).

See the examples below. electron

muon neutrino
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Quarks & Antiquarks

We are only going to consider three quarks.

up quark (u) down quark (d) strange quark (s)

Combinations of quarks form baryons and mesons.

Baryons - always contain 3 quarks. For example a proton contains the quarks, up up down.

Whereas an antiproton contains the quarks, antiup antiup antidown.

Mesons - always contain 2 quarks ( a quark and an antiquark). For example the p +meson

contains the quarks, up and antidown.
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Conservation laws for particle interactions

During particle interactions the following are conserved (the number before the interaction

must equal the number after the interaction).

charge baryon number lepton number strangeness
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Electromagnetic Radiation & Quantum Phenomena

Photoelectric Effect

The photoelectric effect occurs when light above a certain frequency (the threshold

frequency) is shone on metals like zinc, this causes electrons to escape from the zinc. The

escaping electrons are called photoelectrons.

It was shown in experiments that;

the frequency of the light needed to reach a particular minimum value (depending on

the metal) for photoelectrons to start escaping the metal the maximum kinetic energy of the photoelectrons depended on the frequency of the

light not the intensity of the light

The above two observation can only be explained if the electromagnetic waves are emitted

in packets of energy (quanta) called photons, the photoelectric effect can only be explained

by the particle behaviour of light.

The photoelectric equation involves;

h = the Plank constant 6.63 x 10 -34 J s f = the frequency of the incident light in hertz (Hz) f = the work function in joules (J) Ek = the maximum kinetic energy of the emitted electrons in joules (J)

The energy of a photon of light = hf and the work function (f)is the minimum energy

required to remove an electron from the surface of the material. So we can see from the

equation above that if the light does not have a big enough frequency (f) so that the photonhas enough energy to overcome the work function (f) then no photoelectrons will be

emitted.

The above equation can be rearranged into the from y=mx+c
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So plotting a graph of frequency (f) on the x-axis and maximum kinetic energy (E k) on the y-

axis will give a straight line graph. Where the gradient is the Plank constant (h) and the y

intercept is the work function(f), the intercept on the x-axis is the threshold frequency f 0.
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Excitation

The electron volt (eV) is an amount of energy.

It is the amount of energy an electron would gain if it was accelerated through a potential

difference of 1 volt.

1 eV = 1.6 x 10 -19 joules (J) of energy

In atoms electrons orbit the nucleus.

There are particular allowed orbits where electrons can exist without emitting

energy. Electrons can pass between these energy levels. When electrons are given enough

energy to move to higher energy levels they are in an excited state, this is called excitation .

If an electron gets enough energy to remove the electron to infinity this is called ionisation .


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Line Spectra

Emission spectra

A diffraction grating and a spectrometer can be used to look at the emission spectrum froma light source.

If all possible wavelengths of light are present it would look like a continuous spectrum of

colours.

However hot gases emit only particular characteristic colours of light.

Each line in the emission spectrum corresponds to an electron moving from a higher energy

level to a lower energy level. To do this it emits photon of light the energy of the photon of

light is equal to the difference in the energy of the two energy levels.

h = the Plank constant 6.63 x 10 -34 J s f = the frequency of the photon in hertz (Hz) hf = the energy of the photon in joules (J) E1 is the energy of energy level 1 in joules (J) E2 is the energy of energy level 2 in joules (J)

Absorption spectra

When white light passes through a gas the gas absorbs particular wavelengths of light. This

effect can be seen in light from the sun which initially seems like a conscious spectrum but

an closer inspection it can be seen to contain dark lines.
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Wave-particle Duality

Sometimes light behaves like a wave and sometimes light behaves like a particle.

Diffraction can be explained by considering light to be a wave. Photoelectric effect can be explained by considering light to be a particle.

Therefore we use the concept of wave-particle duality when thinking about light.

Momentum

The momentum of a particle can be calculated by multiplying its mass in kilograms (kg) by

its velocity in metres per seconds (m s -1). Momentum is measured in kilogram metres per

second ( kg m s -1 )

momentum = mv

De Broglie wavelength

De Broglie suggested that all particles not just light exhibit wave-particle duality and

therefore it would be possible to calculate the wavelength of particles (the De Brogiel

wavelength).

l = the de Broglie wavelength of the particle in metres (m) h = the Plank constant 6.63 x 10 -34 J s m = mass of the particle in kilograms (kg) v = velocity of the particle in metres per second (m s -1)
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Current Electricity

Charge, Current & Potential Difference

Circuit Symbols - you met these circuit symbols in GCSE Physics.

Conventional current - flows around a circuit from the positive (+) side of the cell to the

negative (-). However the electrons are flowing around the circuit in the opposite direction

from the negative (-) side of the cell to the positive (+).
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Charge, Current & Potential Difference

Charge (Q) charge is measured in coulombs (C).

A single electron carries a charge of 1.6 x 10 -19 C.

Current (I) - is measured in amperes (A).

Current is the rate of flow of charge . A current of 1 A means that 1 coulomb of charge

flows past a point in a circuit every second. ( 1 A = 1 C s -1 ) Current is measured in a

circuit using an ammeter which is placed in series with the component of interest in the

circuit.

I = current in amperes, A DQ = charge in coulombs, C Dt = time in seconds, s

Potential difference (V) - is measured in volts (V).

Potential difference is the work done per unit charge . A potential difference of 1 V

means that 1 joule of work is done per coulomb of charge. ( 1 V = 1 J C -1) Potential

difference in a circuit is measured using a voltmeter which is placed in parallel with the

component of interest in the circuit.

V = potential difference in volts, V W = work done or energy transferred in joules, J Q = charge in coulombs, C

Resistance (W) is the ratio of potential difference across a component to the currentflowing through it, it is measure in ohms (W).

R = resistance in ohms, W

V = potential difference in volts, V I = current in amperes, A
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Examples;

Q1) If all electrons carry a charge of 1.6 x 10 -19 C, how many electrons would be needed to

give a total charge of one coulomb?

Q2) If a current of 0.50 amps flows through a circuit for 120 seconds. How much charge will

have passed into a component in the circuit?

Q3) A charge of 4.0 coulombs was moved through a potential difference of 24 volts, how

much energy was transferred?

Q4) The potential difference across a component is 12 volts and the current through it is

0.37 amps, what is the resistance of the component?
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Current Voltage Characteristics

A resistor at constant temperature (ohmic conductor)

Current is directly proportional to potential difference. Doubling the potential difference

doubles the current in the circuit. The resistance remains the same. Plotting a graph ofpotential difference against current gives a straight line passing through the origin (0,0).

Ohms Law

The electrical current in a conductor is proportional to the potential difference applied toit provided the temperature remains the same.

V = IR

Potential difference = current x resistance

(V, volts V) (I, amps A) (R, ohms W)

Measuring current and potential difference

Current is measure with an ammeter, ammeters are always connected in series with thecomponent of interest.

Potential differences are measured using a voltmeter, voltmeters are connected in parallel

with the component of interest.

By measuring the current and potential difference you can calculate the resistance.
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A Filament Lamp

Here the graph curves because as the filament heats its resistance goes up (the resistance

of the filament is changing).

A diode A diode only allows current to flow in one direction through it (forward biased), when the

current tries to flow the other way (reverse biased) no current is allowed to flow through

the diode.
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When the diode is reversed biased if we keep increasing the potential difference the diodewill eventually begin to conduct in the reverse direction, this is called the break down

voltage.

Thermistor

The resistance of a thermistor decreases as its temperature increases.

Thermistors can be used as thermostats, the thermistor is used in circuits which monitor

and control the temperature of rooms, freezers & fridges etc.
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Thermistors can have a positive or a negative temperature coefficient . A negative

temperature coefficient means that its resistance decreases with an increase in

temperature, this is caused by the release of extra charge carriers in the thermistor.

LDR Light Dependant Resistor

The resistance of an LDR decreases as the light intensity falling on it increases.

LDRs are used in circuits which automatically switch on lights when it gets dark, for example

street lighting.
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Resistivity

The resistance of a piece of wire at a constant temperature depends on both the length of

the wire and the cross-sectional area of the wire.

the longer the wire the greater the resistance the greater the cross-sectional area the smaller the resistance

Resistivity (r) is a property of materials which takes account of their resistance (R), length (L)

and cross-sectional area (A).

Resistivity is measured in ohm metres (W m).

r = the resistivity of the material in Wm R = the resistance of the material in W A = cross-sectional area of the material m 2 L = length of the material in m

Resistivity and temperature In metals increases in temperature make the atoms in the structure of the metal vibrate

more and this makes it more difficult for the electrons to move through the material, so

the resistance of the material goes up. An example of this is the filament bulb .

Here the graph curves because as the filament heats its resistance goes up.
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in semiconducting materials the increase in temperature releases more charge

carriers so the resistance of the materials goes down. An example of this is

the thermistor .

The resistance of a thermistor decreases as its temperature increases, this is a neg ative

temperature coefficient thermistor.

Thermistors can be used as thermostats, the thermistor is used in circuits which monitor

and control the temperature of rooms, freezers & fridges etc.

Superconductivity

In some metals and alloys when the material is cooled to a critical temperature (the critical

temperature varies with the material but an example of the sorts of temperatures

required would be -196 oC) the resistance of the material falls to ZERO . This state of zero

resistance is when the materials become superconducting.

Superconducting materials are used when very strong electromagnets are required, in MRI

scanners or to reduce loses in power cables.
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Example;

Q1) What is the resistance of a piece of wire which is 100 metres long, has a cross-sectional

area of 0.87 x 10 -6 m 2 and has a resistivity of 1.7 x 10 -8 Wm?
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Circuits

Cells in series and in parallel

Cells in Series When cells are connected in series with each other and they are all connected in the same

direction the total potential difference supplied to the circuit is the individual potential

differences added together.

Vtotal = V1 + V2 + V3

Identical cells in parallel with each other

When identical cells are in parallel with each other the total potential difference supplied to

the circuit is equal to the potential difference of just one of the cells.

Vtotal = V1 = V2 = V3 So if three 2V cells are connected in parallel with each other the potential difference

supplied to the circuit is 2V.

Resistors in series and in parallel

Resistors in Series

When resistors are in series with each other there total resistance is just there individual

resistance added together.

Resistors in parallel

When resistors are in parallel with each other there total resistance is found using the

equation below.
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Current in series and parallel circuits

Conservation of charge the total charge flowing into a junction of wires must equal the

total charge flowing out of the junction.

Kirchoffs first law the sum of the currents flowing into a junction of wires must equal the

sum of the currents flowing away from the junction of wires.
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Current in series circuits .

When you put an ammeter into a series circuit the current is the same wherever you put the

ammeter.

Current in parallel circuits .

The total current flowing from the cell towards the branches in the circuit must always

equal the current flowing through each component in the branches of the circuit when they

are added together.
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If the components have different resistances then the current through each component may

be different but it when you add them together they must add up to the total amount of

current leaving the cell.

Potential difference in series and parallel circuits

Kirchoffs second law the sum of the Emfs in any closed loop in a circuit must be equal to

the sum of the potential differences in the closed loop in the circuit.

Potential difference in a series circuit .The total potential difference supplied by the cell is divided up between the components. If

the components all have the same resistance they will have equal amounts of potential

difference across them.
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If the resistance are not equal they may have different amounts of potential difference

across them but when added up they must always equal the p.d. supplied by the cell.

Potential difference in parallel circuits .

The potential difference supplied by the cell is the same potential difference as that across

each component in the parallel circuit.
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Energy & Power in Circuits

Energy (E) is measured in joules (J).

Power (P) is measured in watts (W). Power is the rate at which energy is transferred. One

watt is equal to one joule per second ( 1 W = 1 J s-1

).

E = energy in joules, J V = potential difference in volts,V I = current in amperes, A t = time in seconds, s

P = power in watts, W

V = potential difference in volts, V I = current in amperes, A

P = power in watts, W I = current in amperes, A R = resistance in ohms, W

Examples;

Q1) How much energy is dissipated by a resistor if a potential difference of 9.0V is applied to

it for 331 seconds and a current of 0.23 A flows through it?

Q2) What is the current flowing through a bulb if it has a power of 100W when the potential

difference supplied to it is 230V?
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Q3) What is the power dissipated by a 32 ohm resistor when a current of 1.4 A flows

through it?
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Potential Divider

A potential divider is a simple circuit that uses resisters(or thermistors / LDRs) to supply a

variable potential difference.

They can be used as audio volume controls, to control the temperature in a freezer or

monitor changes in light in a room.

Two resistors divide up the potential difference supplied to them from a cell. The proportion

of the available p.d. that the two resistors get depends on there resistance values.

Vin = p.d. supplied by the cell

Vout = p.d. across the resistor of interest R1 = resistance of resistor of interest R 1 R2= resistance of resistor R 2

Example; use the information in the diagram below to find V out .
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Electromotive Force and Internal Resistance

The electromotive force (e) or e.m.f. is the energy provided by a cell or battery per coulomb

of charge passing through it, it is measured in volts (V). It is equal to the potential

difference across the terminals of the cell when no current is flowing.

e = electromotive force in volts, V E = energy in joules, J

Q = charge in coulombs, C

Batteries and cells have an internal resistance (r) which is measures in ohms (W). When

electricity flows round a circuit the internal resistance of the cell itself resists the flow of

current and so thermal (heat) energy is wasted in the cell itself.

e = electromotive force in volts, V I = current in amperes, A R = resistance of the load in the circuit in ohms, W r = internal resistance of the cell in ohms, W

We can rearrange the above equation;

and then to
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In this equation ( V) appears which is the terminal potential difference , measured in volts

(V). This is the potential difference across the terminals of the cell when current is flowing in

the circuit, it is always less than the E.M.F. of the cell.

Example;

Q1) The p.d. across the terminals of a cell is 3.0 volts when it is not connected to a circuit

and no current is flowing. When the cell is connected to a circuit and a current of 0.37 A is

flowing the terminal p.d. falls to 2.8 V. What is the internal resistance of the cell?

A graph of terminal p.d. against current

If we plot a graph of terminal potential difference (V) against the current in the circuit (I) we

get a straight line with a negative gradient.
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We can them rearrange the e.m.f. equation from above to match the general expression for

a straight line, y = mx +c.

We can see from the red boxes above that;

the intercept on the y-axis is equal to the e.m.f. of the cell the gradient of the graph is equal to -r where r is the internal resistance of the cell.
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Alternating Current (AC)

(DC) direct current

Cells and batteries provide an electrical current which always flows around the circuit in the

same direct, this is called direct current (DC).

(AC) alternating current

In the UK mains electricity is supplied at about 230 volts and is supplied as (AC) or

alternating current. This means the current flows in one direction then the other around the

circuit. The current constantly changes direction (alternates) and so it is called (ac)

alternating current. In the UK the frequency of mains electricity is 50 Hz , this means 50

cycles in one second.

AC signals

We can use an oscilloscope to represent an AC signal.

We can use the oscilloscope trace as a voltmeter if we know what the y-gain is set to on the

oscilloscope. Using the diagram above and knowing that the Y-gain was set to 10 V / div we

can work out that;
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the peak to peak voltage = 6 squares from the highest point to the lowest and each

square is worth 10V. So the peak to peak voltage = 60 V. the peak voltage ( V o )= half the peak to peak voltage = 60 / 2 = 30 V

Once we know the peak voltage ( V o ) and the resistance (R) in the circuit we can calculate

the peak current ( I o ) using the equation V=IR.

Root mean square (rms) values

As the p.d. and current are varying continuously in an AC signal we need to represent an

average value for p.d. and current.

The root mean square values of p.d. ( V rms ) and current ( I rms ) represent the effective value

of the p.d. and current in an AC circuit.

Vrms = root mean square potential difference in volts, V Vo = peak voltage in volts, V

I = root mean square current in amperes, A Io= peak current in amperes, A
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Oscilloscopes

The two controls on an oscilloscope we are interested in are;

Y-gain in volts/division, 1 v/div. Time base in time/division, e.g. 0.002 s/div.

Input connected to ground ( zero volts ) and timebase switched off , oscilloscope trace is a

spot in the middle of the screen.

3 volts from a dc battery ( Y gain set to 1V/div, timebase off ), the oscilloscope trace is a spot

which moves 3 squares (divisions) up.

Input connected to ground ( zero volts ) and timebase switched on , trace appears as a

horizontal line in the middle of the screen.
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3 volts from a dc battery ( Y gain set to 1V/div, timebase on), trace appears as a horizontal

line 3 squares above the middle.

3 volts from an ac power supply ( Y gain set to 1V/div, timebase off ), trace appears as avertical line 6 squares long.

3 volts from an ac power supply ( Y gain set to 1V/div, timebase on 0.002 s/div ), sine like

trace appears.
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The peak voltage (amplitude) is 3V.

The time period (T) is 8 squares x 0.002 = 0.016 s.

We can calculate the frequency (f) in hertz (Hz) using the equation below;

f = 1 divided by 0.016 = 62.5 Hz
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