Download BASIC PHYSICS

BASIC PHYSICS - SURVEY
Stanislav Ďoubal
Quantities, units, standards
The physical quantities are used for quantification and description of physical processes.
Consequently, the methods of measurement must exist for physical quantities. The physical quantity
must be carefully defined and referred to common standards. In other words, the quantities are
measured in units. Units are the scale with which the dimensions are measured. All terms in equation
must have the same dimensions. Units are combination of standards (basic units). Standards are
chosen arbitrarily.
SI systems of units
Standards (basic units)
quantity
basic unit
time
second
abbreviation
s
definition
1 s is 9,192,631,770 period of
radiation during transition of atom Ce133
between two hypefine levels
length
meter
m
1 m is length of path traveled by
light in vacuum during time interval
1/299,792,458 of second
mass
kilogram
kg
defined by platinum-iridium
standard kept in Paris
current
ampere
A
1 A existing in two long, parallel
wires separated 1 m evoked force
per unit of length between the wires
of exactly 2*10  7 N/m
1
temperature
kelvin
K
1 K corresponds to 1/273,16 of
temperature interval between triple
point of water and absolute zero
molar mass
mol
mol
The mole is the amount of substance of a
system which contains as many
elementary entities as there are atoms
in 0.012 kilogram of carbon 12
luminous intensity
candle
cd
The candle is the luminous intensity,
in a given direction, of a source that
emits monochromatic radiation of frequency 540
x 1012 hertz and that has a radiant intensity in that
direction of 1/683 watt per steradian.
Derived units
All other units (than basic) are called derived units. SI of units is a coherent system.
Consequently, the quotient or product of any two SI units in the system yields the SI unit of the
resultant quantity.
Prefixes for SI
symbol
name
amount
E
exa
1018
P
peta
1015
T
tera
1012
G
giga
10 9
M
mega
10 6
k
kilo
10 3
2
c
centi
10  2
m
milli
10  3

micro
10  6
n
nano
10  9
p
pico
10  12
f
femto
10  15
a
atto
10  18
Accepted but not recommended:
h
hecto
10 2
da
deka
101
d
deci
10  1
Dimensions and units
The dimension of quantity is the powers to which the basic units, expressing that quantity are
raised. Example: the dimension of newton (N) is m .kg. s-2 .
Extensive and intensive quantities
Extensive quantities have character of "amount", such as mass, energy, charge. The extent of
extensive quantity of the system is the sum of the amount of this quantity of all subsystems.
Intensive quantities describe "state" and cannot be summarized. Examples of intensive
quantities: concentration, temperature, pressure.
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Scalars and vectors
Scalar quantities are specified by single number (along with the proper unit). Examples: mass,
energy, temperature, charge.
Vector quantities are specified by direction and amount or size. Examples: velocity, force,

displacement. Symbols for vectors: boldface letters or arrow above the letter (A or A )
Graphical addition of vectors
Vector addition does not obey rules of ordinary algebra. The process of addition of vectors is
conveniently expressed in graphical terms, according to Fig. 1.
X2
X3
X1
Fig. 1. Graphical addition of vectors
Vector X3 is the vector sum of vectors X 1 and X 2 . Subtraction of vectors is a reverse
process. Addition of vector obey the associative law, consequently, it is possible to add more than
two vectors in a subsequent way.
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Mechanics
Kinematics
Velocity v
v = dr / dt
(m/s ; m, s),
where r is the vector of displacement, t is the time.
If the movement is in direction x than holds
v = dx / dt.
Speed v
v =  v .
Motion with constant speed
If the motion is in direction of x, then for distance of displacement holds:
x=vt.
Acceleration a
(m / s 2 ; m/s, s)
a = dv/dt
Motion with constant acceleration
v = vo + a t,
where vo is the initial velocity.
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If the motion is in direction of x, then for distance of displacement holds:
x = xo + vot + 1/2 a t 2
Free fall
Free fall is a movement with constant acceleration equal to g = 9,8 m/ s 2 (gravity). If the free
fall is combined with another movement (for instance in projectile motion), the resulting movement
may be calculated as vector sum of these two movements.
Uniform circular motion
For the uniform circular motion (see Fig. 2) the following quantities are defined:
angular speed :
 = d/dt
(rad/s)
frequency f:
f = 1/T,
(Hz or 1/s)
where T is the time for one movement .
Consequently:
 = 2f.
For (centripetal) acceleration a0 holds:
a0 =  2 t = v 2 /r,
where v is the speed of revolution.
Also holds:
v = s/t = 2r/T = 2rf =  r.
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ao
v
ado

r
Fig. 2. Illustration for explanation of circular motion
Harmonic motion
For simple harmonic motion holds (see Fig. 3):
x = A sin (t +  0 ).
Quantity A is the amplitude and  0 is the phase at the time t = 0.
For velocity holds:
v = dx/dt = A  cos (t +  0 ).
For acceleration holds:
a = dv/dt = -  2 A sin (t +  0 ).
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1,5
1
0,5
0
-0,5
-1
-1,5
Fig. 3. Harmonic motion
Dynamics
Newton's first law
Every body continues its state of rest, or in uniform motion in straight line unless it is
compelled to change that state by forces impressed upon it.
Newton's second law
(N; kg, m/ s 2 )
F = m a,
where F is the net force exerted upon the object, m is the mass, a is the acceleration.
Newton's third law
Fab = - Fba.
To every action there is always opposed an equal reaction. A single force cannot exist.
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Newton's law of universal gravitation:
F=
m1m2
r2
,
where F is the gravitational force between two objects,  is the universal constant, m1, m2 are the
masses of the objects, r is the distance between objects.
Gravitational force
F = mg.
Kinetic frictional force (Fig. 4)
v
T
-T
F
N
Fig. 4. Kinetic frictional force
T = f N,
where T is the frictional force, f is the coefficient of kinetic friction, N is the normal force exerted by
the surface.
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Momentum p
p = m v,
(kg.m/s; kg, m)
where m is the mass, v is the velocity.
Also holds:
p = I = F t ,
where I is the impulse of the force F.
Conservation of momentum
pi = p L ,
where p i is the initial momentum, p L is the momentum any later (provided the net external force is
zero).
Centripetal force in uniform circular movement
F = m a0 = m  2 t = m v 2 /r.
Work and energy
W = F.s. cos ,
(J; N, m)
W is the work, F is the force, s is the displacement. The angle  is according Fig. 5.
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F

s
Fig. 5. Illustration to the definition of work
Kinetic energy K
K = 1/2 m v 2 .
Gravitational potential energy U
U = m g h,
m is the mass, g is the gravity, h is the relative height.
Conservation of energy
If the net work of external forces exerted on the system is equal to zero, then the energy of the
system is constant.
Power P
P = dA/dt.
Average power
(W; J, t)
P = A/t.
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Efficiency :
=
W
,
W0
where W is the output energy, W0 is the input energy.
Also holds:
=
P
,
P0
where P is the average output power, P0 is the average input power.
Static
Rigid body
A rigid body is one for which the distance between any pair of points on the object remains
fixed. A rigid body retains its shape and size. In the case of a rigid body, for rotational equilibrium
holds that the effect of force is the same along the line of action. The line of action is the straight line
in the direction of the vector of the force.
Torque about axis M (moment of force about axis)
M = F r = F.. sin,
the meaning of the symbols is according Fig. 6.
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Static equilibrium
Object is in static equilibrium if every point of the object remains in rest. Condition for static
equilibrium: net force must be zero (translation equilibrium) and the external net torque must be zero
(rotational equilibrium).
Translation equilibrium
Object is in translation equilibrium if the acceleration of the center of mass is zero.
Rotational equilibrium
Object is in translation equilibrium if the net external torque is zero:
 M i   Fi ri  0 .
i
i
Center of mass
Center of mass is the point of average position of the mass of the system.
Center of gravity
The point, at which full weight of object can be considered to act.
Calculation of net force applied to an rigid body
Two forces:
a) Line of action with crossing point
The forces are translated along lines of action into crossing point and added according rules
for adding vectors (Fig. 1).
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Fig. 6 Addition of non-parallel forces
b) Parallel forces
Net force is the sum of forces. The position of point of action is calculated with regard to
rotational equilibrium (the net torque is zero).
If there are more forces, the calculation consists in subsequent addition of pairs of forces.
Solids and fluids
Solids
Tensile (normal) stress  and compressive stress
(Pa; N, m 2 )
 = FN /A,
where FN is the force normal to the surface, A is the area.
Shear stress
 = F P /A,
where F P is the force parallel to surface, A is area.
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Pressure p
(Pa; N, m 2 )
p = F/A .
Strain 
 = L/L,
where L is the increase of length, L is the length of unstressed object.
Hooke´s law
For tensile stress holds:
Y=

,
t
where Y is Young´s modulus,  t is the tensile strain.
For shear stress holds:
S=

s
,
where S is shear modulus,  s is the shear strain.
Density 
 = m/V,
where m is the mass, V is the volume.
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Fluids
Pascal's principle
Pressure applied to an enclosed incompressible fluid is transmitted undiminished to all parts
of the fluid.
Static pressure in an incompressible fluid
p = p0 + h  g ,
where p0 is the pressure at the top of the surface, h is the depth,  is the density, g is the acceleration
of gravity.
Archimedes´ principle
A submerged body is buoyed up by the force equal in magnitude to the weight of the displaced
fluid and directed upwards.
Equation of continuity for incompressible fluid
v1 A1 = v 2 A 2 ,
v1is the velocity at the point 1, A1is the area at the point 1, v 2 is the velocity at the point 2, A 2 is the
area at the point 2.
Bernoulli’s equation
p + gh + 1/2  v 2 = constant,
where p is the pressure,  is the density, h is the depth, v is the velocity of the flow of the fluid.
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Waves
Transverse wave
A transverse wave is one in which vector of oscillating quantity (position of particles in case
of sound) is perpendicular to the direction of propagation.
Longitudinal waves
A longitudinal wave is one in which vector of oscillating quantity is parallel to the direction of
propagation.
Wave function for harmonic wave
y = A sin (x/v - t)
where A is the amplitude,  = 2 f is the angular frequency, x is the distance, v is the speed of
propagation, f is the frequency.
Wavelength 
=v/f
Wave number k
k = 2 /
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Wavefront
A wavefront represents a set of points that have the same phase at a given time.
Huygen´s principle
Propagation of a light wave can be determined by assuming that at every point on a wavefront
there arises a spherical wavelet centered on that point.
Snell’s law
The refracted ray is transmitted into the second media, as shown according to following
formula:
sin  n2 v1

 ,
sin  n1 v2
where n1, n2 are the indexes of refraction, v1, v2 are the speeds of propagation.
Critical angle  C
sin  C =
v1
.
v2
Ray that approach the interface with angle less than critical angle are partially reflected and
partially refracted. Rays that approach with angle higher than critical one are totally reflected.
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Sound
Sound waves
Mechanical waves with frequency between frequency about 20 Hz and 20 kHz are called
sound waves. They cause sensation of hearing. The speed of sound waves in the air is about 330m/s.
Sound waves consist in compression and rarefaction of fluid. The sound wave in a fluid is
longitudinal.
Frequency and pitch
For harmonic sound wave, the higher the frequency is, the higher is the perception of pitch.
Intensity of sound I
(W m  2 ; W , m 2 )
I = P/A,
where P is the power of sound, A is the area.
Sound-intensity level s
s = 10 log
I
,
I0
where I 0 is the threshold intensity for human, I 0 = 10  12 W m  2 .
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(dB)
Thermodynamics
Temperature and heat transfer
Temperature
Temperature is proportional to average molecular translation kinetic energy.
Temperature scales
Kelvin scale:
1 kelvin (K) corresponds to 1/273,16 of temperature interval between triple point of water and
absolute zero.
Celsius scale:
1 degree of Celsius (°C ) corresponds to 1/100 of temperature interval between normal boiling and
melting points of water.
Connection between Kelvin and Celsius scales
t C  T  273,15 ,
where t C is the temperature in °C, T is the temperature in K.
Connection between Fahrenheit (t F ) and Celsius ( t C ) scales
t F = 9/5 t C + 32.
t C = 5/9( t F - 32)
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Thermal expansion
a) Linear expansion
L =  L 0 T,
where L is the length change,  is the coefficient of linear expansion, L 0 is the reference length, T
is the temperature interval.
b) Volume expansion
V =  V 0 T,
where  is the coefficient of volume expansion.
The previous formulae hold for moderate temperature changes.
Connection between  and  :
=3
Heat conduction
a) Heat current H
H = Q/t,
(J/s; J, s)
where Q is the heat, t is the time.
b) Steady state heat current along uniform rod
T T
H=kA 2 1,
L
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where k is the thermal conductivity of the material, A is the cross section area, L is the length, T2  T1
is the temperature difference.
Specific heat capacity
a) Specific heat capacity at constant pressure c P
dQ = m c P dT,
where dQ is the infinitesimal change of heat, dT is infinitesimal change of temperature.
b) Specific heat capacity at constant volume cV
dQ = m cV dT
Molar heat capacity
a) Molar heat capacity at constant pressure C P
dQ = n C P dT,
where n is the number of moles.
b) Molar heat capacity at constant volume CV
dQ = n CV dT
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Latent heat
Latent heat L is the amount of heat per unit of mass, which is added to or removed from a
substance undergoing a phase change:
L = Q/m
(J/kg; J, kg)
(Notice that temperature is constant during the phase change).
Work done by a system
dW = p dV
a) Work in isobaric process
W = p V
Laws of thermodynamics
The zeroth law of thermodynamics
Two systems in thermal equilibrium with a third system are in thermal equilibrium with each
other.
The first law of thermodynamics
Q - W = U,
where U is the change in the internal energy of the system.
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The second law of thermodynamics
There exists no cycle, which extracts heat from reservoir at a single temperature and
completely converts it into energy.
The third law of thermodynamics
The absolute zero is the lowest temperature
Ideal gas
Properties of ideal gas
Ideal gas consists of a large number of molecules. The size of the molecules is negligible
compared with the average distance between molecules. The motions of molecules are described by
newtonian dynamics. Molecules move freely, forces between molecules are negligible. All collisions
(between molecules and between molecules and wall) are elastic. The molecules are in a random
motion, and the gas is in equilibrium.
Equation of the state of ideal gas
p V = n R T,
where p is the pressure, V is the volume, n is the number of moles, R is is the universal gas constant,
T is the absolute temperature.
Equation for isobaric processes
V = V0
T
T0
,
where V0, T0 are the reference volume or temperature.
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Equation for isothermal processes
pV = constant
Equation for isochoric processes
P = P0
T
T0
,
where P0 , T0 are the reference pressure or temperature. Volume is constant.
Adiabatic processes
The system is energetically isolated. No heat is transferred to and from the system.
P V  = K,
where K is the constant given by initial state of the system,  =
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CP
.
CV
Electricity and magnetism
Electric field
Electric charge Q
Q = I t,
(C; A, s)
where I is the electric current, t is the time.
Elementary charge e
The elementary charge is the charge of proton. The charge of electron is -e.
e = 1,6 10  19 C
Coulomb´s law
Force between two charges Q A and QB is given by following formula
F=
1
4 
Q A QB
r2
,
where  is the permitivity, r is the distance between charges. If Q A and QB have the same sign, the
force is of a repulsive character. If Q A and QB have an opposite sign, the charges are attracted.
 = r . 0 ,
where 0 is the permitivity of vacuum, r is the relative permitivity of space between charges.
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Electric field intensity E
E = F/Q,
(V/m; N, C)
where F is the force, Q is the charge.
For homogenous field also holds
E = V/d,
where V is the voltage and d is the distance.
Electric potential 
 = A/Q,
(V; J, C)
where A is the electric potential energy.
Voltage V
Voltage is the difference of electric potentials at points 1 and 2
V =  2  1
Capacitors and capacitance
A capacitor consists of two conductors that are insulated from one another. Insulator is referred to as
dielectrics. Capacitor provides temporary storage of charge (Q) and energy. Holds:
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Q = C V,
(C; F, V)
where C is the capacitance, V is the voltage (voltage is the potential difference).
Capacitance of parallel plate capacitor:
C r 0.
A
,
d
A
d
Fig. 7. Parallel plate capacitor
Electric current
The electric current I characterizes flow of charge through material. Holds:
I = dQ /dt, .
(A; C, t)
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Current in one direction is called direct current (dc). Current in a sense back and forth is called
alternating current (ac). For constant dc holds:
I=Q/t.
Electric current in metals
The electric current in metal is flow of (free) electrons in the crystal lattice of the metal.
Resistance and Ohm ´s law
I =V / R,
(A; V,)
(Ohm ´s law)
where I is the current, V is the voltage, R is the resistance. The unit of resistance is ohm ().
Conductance S :
S = 1 / R.
The unit of conductance is siemens (S).
Production of heat (Joule’s law)
W = U I t.
Power dissipated in a resistor
P = V2 / R = I2 R
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1. Kirchhoff´s rule (point rule):
I1
IN
I2
I3
Fig. 8. The point rule: The sum of the currents towards a branch point is equal to the sum of the
currents away from the same branch point
If the currents “towards” are assigned + and the currents “away” -, then holds:
i n
I
i 1
i
0,
2. Kirchhoff´s rule (loop rule):
V1
V2
V3
VN
Fig. 9. The loop rule: The sum of the voltage differences in the round-trip around any closed loop is
zero
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in
V
i 1
i
0.
Resistors in series
R1
R2
RN
RC
Fig. 10. Resistors in series
í n
RC   Ri ,
i 1
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Resistors in parallel
R1
R2
RN
RC
Fig. 11. Resistors in parallel
í n
1 / RC  1/ Ri ,
i 1
Electric current in vacuum
The vacuum is a ideal insulator. The electric current in vacuum is possible only if charged particles
are injected into vacuum. The practically possible ways of injection of charge carriers are as follows:
Thermal electron emission
The carriers are electrons discharged from metallic cathode by thermal movement of electrons
(heating the cathode)
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Photoelectric emission
The carriers are electrons discharged from metallic cathode by photons (elimination of the cathode)
Electric current in gases
The gases are also insulators. The electric current in vacuum is possible only if charged
particles are injected into gas. The practically possible ways of injection of charge carriers are as
follows:
a)
Thermal electron emission
b)
Photoelectric emission
c)
Ionization of the gas (by ionizing radiation or heating the gas)
I
zone of saturation
zone of self-maintained
discharge
zone of recombination
U
Fig. 12. Volt-ampere characteristic of the discharge in gas
Electric current in liquids
The electric current is possible only if carriers are presented in the liquid. The ions are the
carriers in the case of liquid. The dc current causes the electrolysis: The ions are loosing electrons on
anode or accepting electrons on cathode. The carriers are gradually changed into non-charged
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particles. Cations (metal, hydrogen) are eliminating on cathode, anions on cathode. The liquid is
gradually losing the ability to conduct electric current.
For the amount of material (M) accumulating on electrode holds:
M=kQ,
(1. Faraday’s law)
where k, is the electrochemical equivalent, Q is the charge.
For electrochemical equivalent holds:
k
A
,
F .z
(2. Faraday’s law)
where A is the ion mass, F is the Faraday’s constant, z is the number of elementary charges of the ion.
Electric current in semiconductors
Intrinsic semiconductors: Materials with small number of carriers and low conductivity.
Extrinsic semiconductors: Crystal material (as Si, Ge -their atoms have 4 electrons in outer sphere)
with small amount of impurities in the lattice. Impurities: atoms with 3 electrons in outer sphere (P
semiconductors) or atoms with 5 electrons in the outer sphere (N semiconductors).
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Magnetic field
Magnetic induction (B)
F
B
I
Fig. 13. Force on conductor in magnetic fields: direction of the vectors
B
F
,
I .d
(Tesla - T; N, A, m)
where F is the force, I is the current, d the length of conductor.
Force on moving charge in magnetic field (Fig. 14)
F  Q .v  B ,
Magnetic field intensity (H)
H
B
,
r . 0
(A / m)
where r relative permeability of material, 0. is permeability of vacuum.
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F
B
v
Fig. 14. Force on moving charge in magnetic fields: direction of the vectors
Magnetic flux ( )
  B. A ,
(Wb – weber)
where A is the area (perpendicular to vector B)
Magnetic line of force
Magnetic field lines have the direction of vector B, each point.
I
B
N
B
B
S
I
Fig. 14. Magnetic field lines and right hand rule
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Paramagnetic materials: r  1 (slight attenuation of magnetic field and force)
Diamagnetic materials: r  1 (slight amplification of magnetic field and force)
Ferromagnetic materials (Fe, Ni, Co) r  1, (strong amplification of magnetic field and force),
materials for magnets. The relationship between H and B is non-linear, according hysteresis curve.
BF
I
B
HI
Fig. 15. Hysteresis curve
Induced electric field and voltage
u
d
.
dt
where u is the voltage
Inductance (L)
L / I .
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Alternating current
Generators – principle: The coil is revolving magnetic field. The voltage u is induced in the coil
u   N.
d
,
dt
as for  holds:
  B S 0 cos  ,
and
=t
the voltage has sinusoidal character:
u  U 0 sin ( t   0 ) ,
 = .t + O
Fig. 16. Origin of alternating current
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Effective value of sinusoidal voltage (Uef) and current (Ief)
U ef 
Um
,
2
I ef 
Im
,
2
and
where Um and Im are the maximum values.
For energy production P in ac circuits holds:
P = Uef. Ief . t .
Resistor in ac circuits
UR
IR
IR
UR
 =0°
Fig. 17. Resistors: voltage-current relationships
UR / IR = R
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Condenser in ac circuits
iC
uC
90°
/ 2
Fig. 18. Condensers: voltage-current relationships
UC / IC = X C 
1
C
Condensers in serial:
1 / C = 1/C1 + 1/C2 + ....
Condensers in parallel:
C = C1 + C2 + ....
Coil in ac circuits
uL
90°
/ 2
iL
Fig. 19. Coils: voltage-current relationships
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UL / IL = X L   L
Coils in parallel:
1 / L = 1/L1 + 1/L2 + ....
Coils in serial:
L = L1 + L2 + ....
Power (P) in ac circuits
P U I cos ,
where  is the phase shift between I and U
Transformer
Transformer is a device for changing magnitudes of current and voltage. For use in ac circuits only.
N2
N1
I1
U1
U2
I2
Fig. 20. Transformer
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N1
U
I
 1  2 ,
N2
U2
I1
where N1 and N2 are the numbers of loops in the primary and the secondary coils
Optics
The subject of optics is a visible light. The visible light are electromagnetic waves of wavelength
from 400 to 760 nm.
Electromagnetic waves
Transversal waves of vectors B and E. Speed of light in vacuum c = 3 . 108 m/s.
E
c (direction of propagation)
B
Fig. 21. Electromagnetic waves
42
Photons
The light behaves partially like particles: photons.
Energy of photon:
E  h ,
where h is Planck’s constant,  is the frequency of waves.
The color of light
The color of monochromatic light (of one frequency or wavelength) is determined by wavelength.
The red color corresponds to the longest wavelength, the blue color to the shortest wavelength.
Origin of light and emission spectrum
Visible light is emitted during shift of electrons between energy levels in outer sphere of electron
shell of atoms.
Line emission spectrum: emitted from ionized atoms (see Fig.26)
Continuous spectrum: emitted from solids and liquids
43
Survey of electromagnetic waves
wavelength (m)
10 - 16
10 -10
10 -4
gamma rays
X rays
10 +9
TV and radio
UV
10 +6
10 +3
10 +2
VIS
microwaves
IR
10 0
10 -3
energy (eV)
min. ionizing energy
Fig. 22. Survey of electromagnetic waves
Geometrical optics
Fig. 23. Basic rules of geometrical optics: rays in converging lens
44
10 +8
Thin lenses
Power of lens (D):
D
1
,
f
where f is the focal distance.
Lens-maker equation:
1
1
1
,
 / 
a a
f
where a is the distance of object (from lens), a' is the distance of image.
Simple magnifier
The simple magnifier is a converging lens. Angular magnification (M):
M 1 
d
,
f
where d is the near point of the eye, usually d = 0,25 m.
45
Compound light microscope
Fig. 24. Compound light microscope
Magnification:
M
t.d
f OB . f OK
46
optical interval 
object
observer
fOB
fOK
image
eye piece
objective
Fig. 25. Compound light microscope: scheme
Absorption of light - . Lambert’s law
I  I 0 . e  .d ,
where I, I0 are the intensities of light (before and after absorption),  coefficient of absorption
Atoms
Size of atom:
10-9 to 10-10 m, zero charge
Structure of atom:
nucleus (99,95% of mass, + charge, size: 10-14 to 10-15 m)
electron shell (- charge)
Energy levels of electrons- quantum approach
47
The electron in electron shell may be only in certain energy levels (W). The shift between levels leads
to absorption or emission of photon.
Energy of photons:

Wn Ws
h
ionization
limit of series
energy levels
zero state
absorption of photon
emission of photon
hrana série
příklad čárového
spektra (He)
Fig. 26. Line spectrum of atom
Radioactive radiation (origin in nucleus)
4
Alfa particles: nuclei of helium ( 2 He ).
Beta particles: electrons or positrons (plus charged electrons).
Gamma particles: short wave electromagnetic radiation.
48
Radioactive decay
Spontaneous process of change of nucleus.
No
No/2
half-life
T
t
Fig. 27. Kinetics of radioactive decay
Absorption of radioactive radiation
The kinetics of absorption is described by Lambert’s law.
I  I 0 . e  .d ,
49
Io
Io/2
d
half-thickness
Fig. 28. Kinetics of radioactive absorption
50