Electrical Circuits

Last updated Sep 5, 2023 Edit Source

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• Charge is a property of matter
  • It does not have a strong definition
• An object of charge produces an electric field around it
  • Properties of the Electric Field:
    • Extends to infinity
    • Other objects of charge experience an electric force when in the field
    • Has an electric force which decreases with distance from the object
      • This force may be attractive or repulsive
• Static charge refers to how the electric charge is not moving

• 2 Types of Charge: positive and negative
  • Positive
    • e.g. protons, cations, $\alpha$, positrons
  • Negative
    • e.g. electrons, anions
  • The two types of charge behave oppositely
• No charge/charges are balanced: Neutral
  • It itself is not a type of charge
  • e.g. neutron, neutrinos, atoms, etc.

Law of Charges

Opposites attract, likes repel

• Charge is uniformly distributed around charged object
  • $\therefore$ Field lines are evenly distributed around object 450
• Rules:
  • Minimum of 4 field lines
    • Don’t waste time with extra lines; minimise the amount you draw
    • Number of field lines indicate relative density for different objects
  • Must be an arrow going in correct direction
    • Outward for positive
    • Inward for negative
  • Lines must start/finish at the surface of the object
    • Lines should only touch the object, not pierce through
    • They should always come off the particle at right angles even if they will curve later
  • Should start/finish perpendicular to surface

800

• Figure 1. → positively charged object and negatively charged object
  • The electric field flows from the positive object to the negative object
  • Note: This diagram is incorrect because the lines are not spaced evenly and they do not come off at right angles
• Figure 2. → two objects with like charge
  • The electric fields repel each other and leave empty space between the objects
  • Note: This diagram has an inaccuracy because it is missing a line from each particle (from the closest end to each other) which would curve up or down sharply
• Figure 3. → two charged plates with opposite charge
  • The electric field flows from the positive charge plate to the negative charge plate
  • The field is curved on the edges of the plate
• Figure 4. → Charged plate and oppositely charged object
  • Electric field flows from positive object to negative plate (or vice versa)

• Friction will transfer $e^-$ from one surface to another
  • A surface with greater affinity for $e^-$ compared to a second surface, will gain $e^-$ and vice versa
    • Electron affinity is linked with electronegativity
• We cannot tell whether an object has gained positive or negative charge
  • We don’t know which object gains/loses electrons

• Electrons are an easy particle to move, however they move in some materials more freely than others

• Materials where the electrons can move easily are called conductors

  • e.g. metals, water, earth
    • best conductors → good conductors
  • Conductors are good conductors of electricity

• Materials where the electrons have less free movement are called insulators

  • e.g. glass, rubber, plastic, cloth, wood
    • best insulators → good insulators
  • Insulators are poor conductors of electricity
    • Electrons are attracted strongly to atom’s nucleus or are involved in the bonding of the substance
  • No matter how insulating a material is, it still will have some electron movement

• Charging by induction is where electrons are redistributed on an object to produce regions of different charge (i.e. an electric dipole)

  • The separation of charge is temporary and will reverse once the inducing charge is removed
    • This is similar to how temporary dipoles work (from chemistry)
  • This can be observed by using an electroscope
    • An electroscope is a scientific tool that can detect an electric charge on a body
    • It is composed of a pair of metal leaves hanging off a vertical metal rod contained within an insulating box Electroscope

• Charging by conduction is when electrons are physically transferred causing loss/gain of charge

  • This loss/gain of charge is not temporary

• Electrostatically charged objects exert a force upon one another
  • We can calculate the magnitude of this force using Coulomb’s Law
• Coulomb’s Law: $F_e = \frac{k\\ \times\\ q_1q_2}{r^2}$
  • $F_e$ = the electric force acting between the two objects of charge
    • $F_e$ is a vector → either is an attractive force or a repulsive force
      • Two opposite charges → attractive force (towards each other)
      • Two like charges → repulsive force (away from each other)
  • $k$ = constant of proportionality = $9.00 \times 10^9$
    • Measured in $N\\ m^2\\ C^{-2}$ → (not important)
  • $q_1$, $q_2$ = the charges on the two charged objects
    • Measured in coulombs ($C$)
  • $r$ = radius/the distance between the two objects

Charge of Important Particles:

• 1 proton = +$1.6 \times 10^{−19}\\ C$
• 1 electron = -$1.6 \times 10^{−19}\\ C$
• $1\\ C$ = $6.2 \times 10^{18}$ protons/electrons

• A current is a charged particle/s in motion

  • When current is referred to in physics, it is referring to conventional current

• Conventional current is the flow of charge from positive to negative, however, electron current flows from negative to positive

  • This does not make any functional difference in electrical circuits

• When charge moves from one position to another, work is done on the charge

  • i.e. they have changed in their electric potential energy
  • $W = \Delta{E}$
    • Work done ($W$) measured in joules $-$ $J$

• Voltage is the electric force that pushes charged particles over a distance

  • $V = \frac{W}{q}$
    • $q$ = charge ($C$)
  • Voltage is measured in volts $-$ $V$ or $J\\ C^{-1}$
  • If a wire connects two points directly, the voltage between those two points must be the same
    • The last section of a circuit must have a voltage of zero
      • Current adjusts to allow the voltage to always drop to zero at the end of a circuit with fixed resistance
  • A circuit with no resistance will break since there is no point in the circuit for the voltage to drop

• Current is the amount of charge which flows past a given point in a given unit of time (1 second)

  • $I = \frac{q}{\Delta{t}}$
    • $q$ = charge ($C$)
  • Current is measured in amps - $A$
  • Calculating energy from voltage and current → $E = VIt$

• Resistance is the measure of the difficulty with which charge moves through a medium
  • Effective resistance ($R_e$) is equal to total resistance
• Ohm’s Law → $V = IR$
  • $V$ - Voltage drop over component/circuit
    • This measures the change in voltage from the section before the component to after the component
  • $I$ - Current flowing through component/circuit
  • $R$ - Resistance measured in Ohms $(\Omega)$
• Parallel Circuit Formula ($R_e$) → $\frac{1}{R_e} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} +\\ …$
  • For a series circuit, the effective resistance can be found by just adding up all the individual resistances
  • For complex circuits (both parallel and series components), add up all resistances in series and calculated resistance from each individual parallel circuit branch (using parallel circuit formula)
• Ohmic vs Non-Ohmic Devices
  • Ohmic devices have a straight line relationship between increase in voltage and increase in current
  • Non-ohmic devices have a cubic relationship (with one stationary point) between increase in voltage and increase in current
  • Example Graph: OhmicVsNon-Ohmic

• Electrical circuits transform electrical energy into other forms of useful energy
  • e.g. heat, light, sound
• Minimum Components for a Circuit:
  1. Power pack
     • i.e. source of energy/potential
  2. Wire (conducting medium)
     • Made of conductive metals
       • e.g. copper, silver, gold, platinum
  3. Devices/component/resistors

• Series circuits have components attached in a series
• Current is the same in every part of a series circuit
  • If more components (resistors) are added, then the effective current is reduced but will still be the same everywhere
  • $I_{total} = I_1 = I_2 = I_3 = \\ {…}$
• For a single component in series with the energy source, $V \propto emf$
  • If more components are added in series, then the sum of all individual voltage drops equal the total voltage drop
  • $V_{total} = V_1 + V_2 + V_3 +\\ {…}$

• Parallel circuits have branches
• Current is divided among components in different branches
  • $I_{total} = I_1 + I_2 + I_3 +\\ {…}$
• Voltage is the same in each branch
  • $V_{total} = V_1 = V_2 = V_3 =\\ {…}$

• Circuit Diagram Symbols: 600
• Resistor
  • Resistors convert electrical energy to heat energy
    • Voltage falls because work is being done
  • All components in a circuit provide resistance
• Battery
  • Stores chemical energy and converts it to electrical energy
    • The chemical reactions in a battery involve the flow of electrons from one electrode to another
• Voltmeter - measures voltage drop/potential drop/electro motor force
  • Unit ($V$)
• Ammeter - measures current ($I$)
  • Unit ($A$) amperes
• Galvanometer - v. sensitive ammeter