Physics Study Guide/Print version/Section Three

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Physics Study Guide (Print Version)
Units Linear Motion Force Momentum Normal Force and Friction Work Energy
Torque & Circular Motion Fluids Fields Gravity Waves Wave overtones Standing Waves Sound
Thermodynamics Electricity Magnetism Optics
Physical Constants Frictional Coefficients Greek Alphabet Logarithms Vectors and Scalars Other Topics

Contents

Introduction[edit]

Thermodynamics deals with the movement of heat and its conversion to mechanical and electrical energy among others.

Laws of Thermodynamics[edit]

First Law[edit]

The First Law is a statement of conservation of energy law:


\Delta U = Q - W

The First Law can be expressed as the change in internal energy of a system (\Delta U) equals the amount of energy added to a system (Q), such as heat, minus the work expended by the system on its surroundings (W).

If Q is positive, the system has gained energy (by heating).

If W is positive, the system has lost energy from doing work on its surroundings.

As written the equations have a problem in that neither Q or W are state functions or quantities which can be known by direct measurement without knowing the history of the system.

In a gas, the first law can be written in terms of state functions as


dU = T ds - p dV

Zero-th Law[edit]

After the first law of Thermodynamics had been named, physicists realised that there was another more fundamental law, which they termed the 'zero-th'.

This is that:


If two bodies are at the same temperature, there is no resultant heat flow between them.

An alternate form of the 'zero-th' law can be described:


If two bodies are in thermal equilibrium with a third, all are in thermal equilibrium with each other.

This second statement, in turn, gives rise to a definition of Temperature (T):


Temperature is the only thing that is the same between two otherwise unlike bodies that are in thermal equilibrium with each other.

Second Law[edit]

This law states that heat will never of itself flow from a cold object to a hot object.


S = k_B \cdot ln(\Omega)

where k_B is the Boltzmann constant (k_B = 1.380658 \cdot 10^{-23}  \mbox{ kg m}^2 \mbox{ s}^{-2} \mbox{ K}^{-1}) and \Omega is the partition function, i. e. the number of all possible states in the system.

This was the statistical definition of entropy, there is also a "macroscopic" definition:


S = \int  \frac{\mathrm{d}Q}{T}

where T is the temperature and dQ is the increment in energy of the system.

Third Law[edit]

The third law states that a temperature of absolute zero cannot be reached.

Temperature Scales[edit]

There are several different scales used to measure temperature. Those you will most often come across in physics are degrees Celsius and kelvins.

Celsius temperatures use the symbol Θ. The symbol for degrees Celsius is °C. Kelvin temperatures use the symbol T. The symbol for kelvins is K.


The Celsius Scale[edit]

The Celsius scale is based on the melting and boiling points of water.

The temperature for freezing water is 0 °C. This is called the freezing point


The temperature of boiling water is 100 °C. This is called the steam point.


The Celsius scale is sometimes known as 'Centigrade', but the CGPM chose degrees Celsius from among the three names then in use way back in 1948, and centesimal and centigrade should no longer be used. See Wikipedia for more details.

The Kelvin Scale[edit]

The Kelvin scale is based on a more fundamental temperature than the melting point of ice. This is absolute zero (equivalent to −273.15 °C), the lowest possible temperature anything could be cooled to—where the kinetic energy of any system is at its minimum. The Kelvin scale was developed from an observation on how the pressure and volume of a sample of gas changes with temperature- PV/T is a constant. If the temperature ( T)was reduced, then the pressure ( P) exerted by Volume (V) the Gas would also reduce, in direct proportion. This is a simple experiment and can be carried out in most school labs. Gases were assumed to exert no pressure at -273 degree Celsius. ( In fact all gases will have condensed into liquids or solids at a somewhat higher temperature)

Although the Kelvin scale starts at a different point to Celsius, its units are of exactly the same size.

Therefore:


Temperature in kelvins (K) = Temperature in degrees Celsius (°C) + 273.15

Specific Latent Heat[edit]

Energy is needed to break bonds when a substance changes state. This energy is sometimes called the latent heat. Temperature remains constant during changes of state.

To calculate the energy needed for a change of state, the following equation is used:


Heat transferred, ΔQ (J) = Mass, m (kg) x specific latent heat capacity, L (J/kg)

The specific latent heat, L, is the energy needed to change the state of 1 kg of the substance without changing the temperature.

The latent heat of fusion refers to melting. The latent heat of vapourisation refers to boiling.

Specific Heat Capacity[edit]

The specific heat capacity is the energy needed to raise the temperature of a given mass by a certain temperature.

The change in temperature of a substance being heated or cooled depends on the mass of the substance and on how much energy is put in. However, it also depends on the properties of that given substance. How this affects temperature variation is expressed by the substance's specific heat capacity (c). This is measured in J/(kg·K) in SI units.


Change in internal energy, ΔU (J) = mass, m (kg) x specific heat capacity, c (J/(kg·K)) x temperature change, ΔT (K)

Physics Study Guide (Print Version)
Units Linear Motion Force Momentum Normal Force and Friction Work Energy
Torque & Circular Motion Fluids Fields Gravity Waves Wave overtones Standing Waves Sound
Thermodynamics Electricity Magnetism Optics
Physical Constants Frictional Coefficients Greek Alphabet Logarithms Vectors and Scalars Other Topics

Electricity[edit]

F = \frac{k\cdot q_1\cdot q_2}{r^2}

The force resulting from two nearby charges is equal to k times charge one times charge two divided by the square of the distance between the charges.


E = \frac{F}{q}

The electric field created by a charge is equal to the force generated divided by the charge.


E = \frac{k\cdot q}{r^2}

Electric field is equal to a constant, “k”, times the charge divided by the square of the distance between the charge and the point in question.


U = \frac{k\cdot q_1\cdot q_2}{r}

Electric potential energy is equal to a constant, “k” multiplied by the two charges and divided by the distance between the charges.


Variables


F: Force (N)
k: a constant, 8.988×109 (N·m2/C2)
q1: charge one (C)
q2: charge two (C)
r: distance between the two charges, (m)


Electricity acts as if all matter were divided into four categories:

  1. Superconductors, which allow current to flow with no resistance. (However these have only been produced in relatively extreme laboratory conditions, such as at temperatures approaching absolute zero)
  2. Conductors, which allow electric current to flow with little resistance.
  3. Semiconductors, which allow some electric current to flow but with significant resistance.
  4. Insulators, which do not allow electric current to flow.

Charges are positive (+) or negative (-). Any two like charges repel each other, and opposite charges attract each other.

Electric fields[edit]

A charge in an electrical field feels a force. The charge is not a vector, but force is a vector, and so is the electric field. If a charge is positive, then force and the electric field point in the same direction. If the charge is negative, then the electric field and force vectors point in opposite directions.

A point charge in space causes an electric field. The field is stronger closer to the point and weaker farther away.

Electricity is made of subatomic particles called Electrons and so are Electric Fields and Magnetic Fields.

  • For a good introduction to Gauss' Law and Ampere's Law, check out this website
Physics Study Guide (Print Version)
Units Linear Motion Force Momentum Normal Force and Friction Work Energy
Torque & Circular Motion Fluids Fields Gravity Waves Wave overtones Standing Waves Sound
Thermodynamics Electricity Magnetism Optics
Physical Constants Frictional Coefficients Greek Alphabet Logarithms Vectors and Scalars Other Topics

Magnetism[edit]

\boldsymbol{F}_B=q\boldsymbol{v}\times\boldsymbol{B}

The magnetic force exerted on a moving particle in a magnetic field is the cross product of the magnetic field and the velocity of the particle, multiplied by the charge of the particle.


Because the magnetic force is perpendicular to the particle's velocity, this causes uniform circular motion. That motion can be explained by the following

r=\frac{mv}{qB}

The radius of this circle is directly proportional to the mass and the velocity of the particle and inversely proportional to the charge of the particle and the field strength of the magnetic field.

T = \frac{2\pi m}{qB}
f = \frac{qB}{2\pi m} = \frac{v}{2\pi r}

The period and frequency of this motion (referred to as the cyclotron period and frequency) can be derived as well.


B = \frac{\mu_0I}{2\pi y}

The magnetic field created by charge flowing through a straight wire is equal to a constant, \frac{\mu_0}{2\pi}, multiplied by the current flowing through the wire and divide by the distance from the wire.

B = \frac{\mu_0 \mu}{4\pi x^{3}}

The magnetic field created by a magnetic dipole (at distances much greater than the size of the dipole) is approximately equal to a constant, \frac{\mu_0}{4\pi}, multiplied by the dipole moment divided by the cube of the distance from the dipole. EDIT: This forumla is incomplete. The field from a dipole is a vector that depends not only on the distance from the dipole, but also the angle relative to the orientation of the magnetic moment. This is because of the vector nature of the magnetic moment and its associated magnetic field. The field component pointing in the same directions as the magnetic moment is the above formula multiplied by (3*(Cos[theta])^2-1).

B = \mu_0 n I

The magnetic field created by an ideal solenoid is equal to a constant, \mu_0, times the number of turns of the solenoid times the current flowing through the solenoid.

B = \frac{\mu_0 n I}{2\pi r}

The magnetic field created by an ideal toroid is equal to a constant, \mu_0, times the number of turns of the toroid times the current flowing through the toroid divided by the circumference of the toroid.


F_B = \frac{\mu_0 I_1 I_2 \ell}{2\pi d}

The magnetic force between two wires is equal to a constant, \frac{\mu_0}{2\pi}, times the current in one wire times the current in the other wire times the length of the wires divided by the distance between the wires.

\tau = I\vec A\times\vec B

The torque on a current loop in a magnetic field is equal to the cross product of the magnetic field and the area enclosed by the current loop (the area vector is perpendicular to the current loop).


\vec \mu = I\vec An

The dipole moment of a current loop is equal to the current in the loop times the area of the loop times the number of turns of the loop.


U_B = -\vec\mu\cdot\vec B

The magnetic potential energy is the opposite of the dot product of the magnetic field and the dipole moment.


Variables


F: Force (N)
q: Charge (C)
v: Velocity (m/s)
B: Magnetic field (teslas (T))
r: Radius (m)
m: Mass (kg)
T: Period (s)
f: Frequency (Hz)
\mu_0: A constant, 4π×10-7 N/A
y: Distance (m)
\mu: Dipole moment
x: Distance (m)
n: Number of turns
\ell: Length (m)
d: Distance (m)
\tau: Torque (N·m)
A: Area (m2)
U: Potential energy (J)

Physics Study Guide (Print Version)
Units Linear Motion Force Momentum Normal Force and Friction Work Energy
Torque & Circular Motion Fluids Fields Gravity Waves Wave overtones Standing Waves Sound
Thermodynamics Electricity Magnetism Optics
Physical Constants Frictional Coefficients Greek Alphabet Logarithms Vectors and Scalars Other Topics

Electronics is the application of electromagnetic (and quantum) theory to construct devices that can perform useful tasks, from as simple as electrical heaters or light bulbs to as complex as the Large Hadron Collider.

Section Three;component of electronics

Electronics

Introduction[edit]

To discuss electronics we need the basic concepts from electricity: charge, current which is flow of charge, and potential which is the potential energy difference between two places. Please make sure these concepts are familiar before continuing.

Circuits[edit]

The interest of electronics is circuits. A circuit consists of wires that connect components. Typical components are resistors, voltage sources and so on, which will be discussed later. A circuit can be open, when there is a break so that no current can flow, or it can be closed, so that current can flow. These definitions allow us to discuss electronics efficiently.

Direct current and alternating current[edit]

Basic components[edit]

Ohm's law[edit]

IF 'V' IS POTENTIAL DIFFERENCE APPLIED AT TWO ENDS OF CONDUCTOR AND 'I' IS CURRENT FLOWING THROUGH THE CONDUCTOR THEN 'I' IS DIRECTLY PROPORTION TO ITS 'V' V = I x R

Kirchoff's laws[edit]

Kirchoff's laws generally hold for direct current (DC) circuits, but fail when dealing with changing electric current and voltage such as alternating current (AC) or signal processing in combination with capacitors, inductors, and antennas.

Kirchoff's current law[edit]

The sum of all the currents entering and leaving any point in a circuit is equal to zero.

\sum_{k=1}^n I_k = 0

It is based on the assumption that current flows only in conductors, and that whenever current flows into one end of a conductor it immediately flows out the other end.

Kirchoff's voltage law[edit]

The sum of all the voltages around the circuit loop is equal to zero.

\sum_{k=1}^n V_k = 0

It is based on the assumption that there is no fluctuating magnetic field linking the closed circuit loop.

Power[edit]

p=work done/time taken p=I*V (current * Voltage)

Resistors in series[edit]

Req=R1+R2+R3+--------

Resistors in parallel[edit]

1/R = 1/R1+1/R2+1/R3+......

Superposition of sources[edit]

Capacitors[edit]

C={Q\over V}
C_{\rm series}=\sum_n{1\over C_n}={1\over C_1}+{1\over C_2}+{1\over C_3}+\cdots+{1\over C_n}
C_{\rm parallel}=\sum_n C_n=C_1+C_2+C_3+\cdots+C_n

Inductances[edit]

Frequency-dependent circuits[edit]

Semiconductors[edit]

I = \frac{Q}{T}

Current is the rate of flow of charge.

I = Current [amperes - A]
Q = Charge [coulombs - C]
T = Time [seconds - s]

V = IR\

howstuffworks.com

Voltage is equal to current multiplied by resistance

Power is equal to the product of voltage and current

Electronics is the flow of current through semiconductor devices like silicon and germanium.

Semiconductor devices are those which behave like conductors at higher temperature.

Transistor, diode, SCR are some electronic devices.

Physics Study Guide (Print Version)
Units Linear Motion Force Momentum Normal Force and Friction Work Energy
Torque & Circular Motion Fluids Fields Gravity Waves Wave overtones Standing Waves Sound
Thermodynamics Electricity Magnetism Optics
Physical Constants Frictional Coefficients Greek Alphabet Logarithms Vectors and Scalars Other Topics

Light[edit]

Light is that range of electromagnetic energy that is visible to the human eye, the visible colors. The optical radiation includes not only the visible range, but a broader range of invisible electromagnetic radiation that could be influenced in its radiation behavior in a similar way as the visible radiation, but needs often other transmitters or receivers for this radiation. Dependant on the kind of experimental question light - optical radiation behaves as a wave or a particle named lightwave or photon. The birth or death of photons needs electrons - electromagnetic charges, that change their energy.


The speed of light is fastest in the vacuum.

c\approx 3\cdot 10^8 \mbox{ m s}^{-1}

In a wave we have to distinguish between the speed of transport of energy or the speed of the transport of on phase state of a wave of a defined frequency. In vacuum the speed of waves of any photon energy - wavelength is the same, but the transmission speed through material is dependent on wavelength - photon energy. At the time the measurement of the speed of light in vacuum reached the uncertainty of the unit of length, the meter, this basic unit got in 1960 a new definition, based on the unit of time. Taking the best known measurement values it was defined without any uncertainties of length, that the speed of light is 299,792,458 meters per second. For this reason the only uncertainty in the speed of light is the uncertainty of the realization of the unit of time, the second. (If you like to get the standard of length, cooperate with the watchmaker).

However, when electromagnetic radiation enters a medium with refractive index, n, its speed would become

c_n=\frac{c}{n}

where c_n is the speed of light in the medium.

Refraction[edit]

Refraction occurs when light travels from one medium into another (i.e. from air into water). Refraction is the changing of direction of light due to the changing speed of light. Refraction occurs toward the normal when light travels from a medium into a denser medium. Example when light travels from air into a block of glass, light is refracted towards the normal. The ratio between the sine of the angle of the incident ray and sine of the angle of the refracted ray is the same as the ratios of the indexes of refraction.

\frac{\sin\theta_i}{\sin\theta_r} = \frac{n_r}{n_i} \quad \text{or} \quad n_i\sin\theta_i = n_r\sin\theta_r\

This is known as Snell's Law - an easy way to remember this is that 'Snell' is 'lens' backwards.

Mirrors and lenses[edit]

Focal length[edit]

\frac {1}{d_i} + \frac {1}{d_o} = \frac {1}{f}
  • f is the focal length.
    • f is negative in convex mirror and concave lens.
    • f is positive in concave mirror and convex lens.
  • d_i is the distance from the image to the mirror or lens
    • For a mirror, it is positive if the image appears in front of the mirror. It is negative if the image appears behind.
    • For a lens, it is positive if the image appears on the opposite side of the lens as the light source. It is negative if the image appears on the same side of the lens as the light source.
  • d_o is the distance from the object to the mirror or the lens (always positive). The only case, when it is negative, is the case, when you don't have a real object, but you do have an imaginary object - a converging set of rays from another optical system.
  • an easy way to remember the formula is to memorize "if I Do I Die", which stands for 1/f = 1/d_0 + 1/d_i

Magnification[edit]

M = \frac {h_i}{h_o} =-\frac {d_i}{d_o}
  • M is the magnification.
    • If it is positive the image is upright
    • If it is negative the image is inverted
  • h_i is the image height.
  • h_o is the object height.
  • d_i is the distance from the image to the mirror or lens (also often v)
    • For a mirror, it is positive if the image appears in front of the mirror. It is negative if the image appears behind.
    • For a lens, it is positive if the image appears on the opposite side of the lens as the light source. It is negative if the image appears on the same side of the lens as the light source.
  • d_o is the distance from the object to the mirror or lens (also often u)