Physics Study Guide/Print version/Section Three

Introduction

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

Laws of Thermodynamics

First Law

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

$dU=Tds-pdV$

Zero-th Law

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

This law states that heat will never 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

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

Temperature Scales

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

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

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

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

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)

Electricity

$F={\frac {k\cdot q_{1}\cdot q_{2}}{r^{2}}}$

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. This what force of attraction between to charged particle says, according to coulomb's law.

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$E={\frac {F}{q}}$

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

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

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.

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$U={\frac {k\cdot q_{1}\cdot q_{2}}{r}}$

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

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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

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. One must also note that electrical fields come under the category of spherical fields as the inverse square law may be applied to the electrical field. This means that the electrical force, exhibited by the electrical field emitted by the subatomic electron charge (-), acting upon a body is inversely proportional to the distance between the center point of the electric field (subatomic electron) and the body on which the electric force is acting upon.

An electric circuit is composed of conducting wires (through which an electric current flows through), a key or switch which is utilized to open and close the circuit, components which transfer electrical energy to a form of energy required by the component and an electromotive source (such as a voltaic cell). A voltaic cell is an electromotive source in which are present two plates, zinc and copper, placed in dilute sulphuric acid. Whence the circuit is closed the zinc reacts with the sulphuric acid to produce zinc sulphate. The electromotive force which discharges the electrical energy in the electric current is considered to be originated on the surface of the zinc plate in the voltaic cell. However, depending upon the cell, closing the circuit gives rise to polarization, accumulation of hydrogen bubbles on the surface of the copper plate which seriously interferes with the movement of electricity and reduces the magnitude of the electromotive force. For this reason Leclanché cells are utilized. Consisting of similar characteristics as that of the voltaic cell however a Mage difference is present. Instead of the use of copper plates, a carbon plate is used. For this reason, magneze dioxide may be placed on the carbon to react to form a compound which whence in contact with hydrogen bubbles will turn the hydrogen into water, hence increasing the size of the electromotive force produced by the cell. The resistance encountered in conducting wires: Inversely proportional to the diameter of the conducting wire. Directly proportional to the length of the conducting wire. Varies with different substances. Varies with temperature of the conducting wire.

In order to maintain a constant flow of an electric current a constant expenditure of chemical or mechanical energy is required. An electric current is accompanied by an electric field and a magnetic field. A device employed into determining the presence of an electric current is known as a galvanoscope. The conducting wire through which the electric current flows through is he led over and parallel to the galvanoscope the magnetoscope preset inside of the galvanoscope being deflected in the opposite direction to which the electric current flows in. So with the aid of a galvanoscope one may not only deduce the magnetic properties of an electric current, the exhibition of a magnetic field, but the direction in which the current flows through. An electromotive force may also be generators by a dynamo. A rotating magnet present inside of a helix. The magnetic properties of electric currents may be used to construct magnets. An electromagnet is commonly described as a mass of iron on which is placed a helix/solenoid through which flows an electric current. The magnetic field emitted by the electric current is increased if the solenoid is placed around a magnetic mass of iron or any other substance possessing magnetic properties, that is the magnetic field of the iron is added to that of the electic current producing a more powerful magnetic field. Conductors may be arranged in two variants. Series and parallel circuits. In series, the current passes through each conductor in turn, where Ohm's law changes to I = nE/(nr + R), where I is the current intensity, n is the number of cells arranged in series in the circuit, E is the electromotive force applied to the circuit, r is the internal resistance ( the resistance the current that is produced in the cell experiences whence passing from the zinc plate to the copper or carbon plate through the sulphuric acid ) and R is the external resistance.

• For a good introduction to Gauss' Law and Ampere's Law, check out this website

Magnetism

${\boldsymbol {F}}_{B}=q{\boldsymbol {v}}\times {\boldsymbol {B}}$

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.

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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.

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$B={\frac {\mu _{0}I}{2\pi y}}$

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).

$B=\mu _{0}nI$

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.

$B={\frac {\mu _{0}nI}{2\pi r}}$

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.

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$F_{B}={\frac {\mu _{0}I_{1}I_{2}\ell }{2\pi d}}$

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).

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${\vec {\mu }}=I{\vec {A}}n$

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.

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$U_{B}=-{\vec {\mu }}\cdot {\vec {B}}$

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)

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

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

The interest of electronics is circuits. A circuit consists of wires that connect components. Typical components are resistors, voltage sources. In order to maintain a constant electrical current a continued exhaustion of chemical or mechanical energy is required.

A voltaic cell is a common electromotive power source for a circuit. It consists primarily of two plates, a positive copper plate and a negative zinc plate. One must note that the plates are placed in dilute sulfuric acid. Whence a key is switched or the circuit is closed the zinc reacts with the sulfuric in which it is placed in. One may discern that the electromotive force which is then applied to the circuit is believed to be converted from chemical to electrical energy upon the surface of the zinc cell. Whence the E.M.F is converted from chemical to electrical energy the electromotive force travels through the sulfuric acid. However disadvantages occur whence utilizing a voltaic or galvanic cell. Whence the circuit is closed, simultaneously hydrogen bubbles accumulate upon the copper plate surface hence decreasing the total electromotive power source applied to the circuit in question. The resistance with which the electromotive source encounters as it flows form the zinc plate to the copper plate through the dilute sulfuric acid is distinguished as internal resistance. Hence the voltaic cell uses diluted rather than concentrated sulfuric acid so as to reduce the internal resistance present inside of the component which applies the electromotive force to the circuit.

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

When the Electrons moves through a particular medium in straight without oscillating on their mean position then it is Direct Current. This DC is used in almost every electronical component. Alternating Current on the other hand as the name suggest, the Electrons alter back and forth and hence produces much electrical energy. AC is mainly used to reduce the wastage of electrons and passing much energy at one time.

Ohm's law

If 'V' is Potential Difference applied at two ends of conductor and 'I' is Current flowing through the conductor then 'I' is directly proportional to its 'V'. V = I x R

Kirchoff's laws

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

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

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

p=work done/time taken p=I*V (current * Voltage) Other Equations for P can also be derived using Ohm's Law, such as P = IR^2, because V=IR, which can be plugged in to get P= I * (IR) and another equation being P = V^2/R.

Resistors in series

In a series circuit, resistance increases as more resistors are added.Each resistor makes an addition to the restriction of the flow of charge.The current through the battery is inversely proportional to the total resistance. The equivalent(total) resistance is calculated by adding the resistances together. R$eq$=R$1$+R$2$+R$3$+--------

Resistors in parallel

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

Capacitors

$C={Q \over V}$

$C_{\rm {series}}=\sum _{n}{1 \over C_{n}}={1 \over C_{1}}+{1 \over C_{2}}+{1 \over C_{3}}+\cdots +{1 \over C_{n}}$

$C_{\rm {parallel}}=\sum _{n}C_{n}=C_{1}+C_{2}+C_{3}+\cdots +C_{n}$

Semiconductors

$I={\frac {Q}{T}}$

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.

Light

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. Dependent 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.

$c=299,792,458{\frac {m}{s}}$

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

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

Focal length

${\frac {1}{d_{i}}}+{\frac {1}{d_{o}}}={\frac {1}{f}}$

• $f$ 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

$M={\frac {h_{i}}{h_{o}}}=-{\frac {d_{i}}{d_{o}}}$

• $M$ 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 $u$)