Comprehensive Study Guide: Electrical Circuits, Charge, and Resistance

Types of Charges: There are three primary types of electrical charges found in atoms: * Protons: Positively charged particles ( $e+$ ). * Electrons: Negatively charged particles ( $e-$ ). * Neutrons: Particles with no net charge (neutral).
Charge Interactions: * Opposite charges attract one another. * Like charges repel one another.
The Atom: * An atom consists of a nucleus containing protons and neutrons, with electrons orbiting the nucleus in shells. * Valence electrons are those in the outermost shell. In metal atoms, these electrons are not tightly bound to the nuclei. They are delocalized and free to move throughout the entire structure.
Changes in Net Charge: * Atoms gain or lose electrons to become charged (ions). They cannot gain or lose protons because protons are located in the nucleus, whereas electrons are in outer shells and more easily transferred. * Gaining Electrons: An atom that gains $2$ electrons will have a net charge of $-2$ . * Losing Electrons: An atom that loses $3$ electrons will have a net charge of $+3$ .

Elementary Charge ( $e$ ): This is the size of the charge on a single proton ( $1.6 imes 10^{-19} C$ ) or electron ( $-1.6 imes 10^{-19} C$ ).
The Coulomb ( $C$ ): Because elementary charge is extremely small, charge ( $Q$ ) is measured in Coulombs. * $1 ext{ Coulomb} = 6.25 imes 10^{18}$ protons or electrons.
Calculations of Charge: 1. Charge of 4 million electrons: $Q = rac{4 imes 10^6 ext{ electrons}}{6.25 imes 10^{18} ext{ electrons/C}}$ 2. Charge of 2.4 trillion electrons: $Q = rac{2.4 imes 10^{12} ext{ electrons}}{6.25 imes 10^{18} ext{ electrons/C}}$ 3. Electrons in $-6 ext{ µ}C$ : $ext{Number of electrons} = 6 imes 10^{-6} C imes 6.25 imes 10^{18} ext{ electrons/C} = 3.75 imes 10^{13} ext{ electrons}$ 4. Transfer from a net charge of $2 ext{ µ}C$ : * $ ext{Electrons transferred} = 2 imes 10^{-6} C imes 6.25 imes 10^{18} = 1.25 imes 10^{13}$ electrons. * Because the charge is positive ( $+2 ext{ µ}C$ ), the electrons were lost.

Conductors: Materials (like Copper, $Cu$ ; Sodium, $Na$ ; Magnesium, $Mg$ ) that allow charge to move freely. Metals have valence electrons that are not tightly bound and move when a potential difference is applied.
Insulators: Materials (like plastic) where electrons are tightly bound to their nuclei and are not free to move even when a potential difference is applied.
Delocalization: In metals, electrons from the outer shell are delocalized; they are free to move throughout the structure, which is why metals are good conductors.

Cell: A single unit of electrical energy.
Battery: A collection of two or more cells. (A battery made of 3 cells would show three cell symbols in sequence).
Lamp: A component that transforms electrical energy into light.
Resistor: A component designed to provide resistance.
Variable Resistor: A resistor whose resistance can be adjusted.
Ammeter: Measures current; must be connected in series.
Voltmeter: Measures potential difference; must be connected in parallel across a component.
Switch: Can be open (breaks circuit) or closed (completes circuit).
Fuse: A safety device that breaks the circuit if the current is too high.
LED (Light Emitting Diode): A diode that emits light and only allows current to flow in one direction.
LDR (Light Dependent Resistor): Resistance changes based on light intensity.
Thermistor: Resistance changes based on temperature.

Electric Current ( $I$ ): The flow of electric charge. It is the amount of charge ( $Q$ ) passing a point in one second ( $t$ ). * Unit: Amperes or Amps ( $A$ ). * Formula: $I = rac{Q}{t}$ * Measurement: Use an ammeter connected in series so all charges pass through it. * Direction: Conventional current flows from positive to negative, while electron flow is from negative to positive.
Potential Difference ( $V$ ): The change in electrical potential energy ( $E$ ) of a charge between two points. It is often described as the 'push' from a power supply. * Unit: Volts ( $V$ ). * Formula: $V = rac{E}{Q}$ * Measurement: Use a voltmeter connected in parallel to measure energy before and after a component.
Power ( $P$ ): The rate at which energy is transferred. * Unit: Watts ( $W$ ). $1 ext{ Watt} = 1 ext{ J/s}$ . * Formulas: $P = rac{E}{t}$ or $P = V imes I$ .

Resistance ( $R$ ): A measure of how difficult it is for charge to flow through a material. * Unit: Ohms ( $Ω$ ). * Formula: $R = rac{V}{I}$ .
Ohm’s Law: If temperature remains constant, the potential difference across a wire is directly proportional to the current through it ( $V = IR$ ).
Ohmic Conductors: Materials that obey Ohm's Law and maintain constant resistance as potential difference or current changes.
Non-Ohmic Conductors: Materials where resistance changes depending on the potential difference or current (e.g., filament lamps, diodes). * Filament Lamp: As potential difference increases, the current increases at a slower rate. This is because the metal atoms in the lattice vibrate more as the temperature increases, causing more collisions with electrons and increasing resistance. * Diode/LED: These have massive resistance in the reverse direction, meaning no current flows backwards. They only allow current to flow in one direction.

Series Circuits: Components are connected one after another in a single loop. * Current: The same at any point ( $I_1 = I_2 = I_3$ ). * Potential Difference: Shared between components. The sum of voltages across components equals the power supply voltage ( $V_{source} = V_1 + V_2 + …$ ). * Resistance: Resistance adds up. Multiple resistors increase total resistance because current is reduced while PD stays same ( $R_{eq} = R_1 + R_2 + …$ ).
Parallel Circuits: Components are connected alongside one another in different loops or branches. * Current: Split between branches. Total current is the sum of currents in each branch (Kirchhoff’s Junction Rule: Current in = Current out). * Potential Difference: The same across each branch and equal to the power supply ( $V_{source} = V_1 = V_2 = …$ ). Resistance: Adding more resistors in parallel reduces the total resistance. There are more pathways for the current, so the total current increases. The total resistance is always less than the smallest individual resistor (… $rac{1}{R_{eq}} = rac{1}{R_1} + rac{1}{R_2} + …$ ).

Q: Why do atoms gain/lose electrons but not protons? * A: Electrons are on the outside of the atom and can be easily transferred. Protons are in the nucleus and held by strong forces.
Q: What is the charge of an atom that lost 2 electrons? * A: $+2$ .
Q: How many amps in $4 ext{ kA}$ ? * A: $4000 ext{ A}$ .
Q: How many amps in $2800 ext{ mA}$ ? * A: $2.8 ext{ A}$ .
Q: Calculate resistance for a thermistor with current $3.5 ext{ mA}$ and potential difference $4.2 ext{ V}$ . * A: $R = rac{4.2}{3.5 imes 10^{-3}} = 1200 ext{ Ω}$ .
Q: Calculate charge for that thermistor in 5 minutes. * A: $Q = I imes t = 0.0035 ext{ A} imes (5 imes 60 ext{ s}) = 1.05 ext{ C}$ .
Q: What happens to total resistance if another resistor is added to a series circuit? * A: The total resistance increases because $R_{eq} = R_1 + R_2 + R_3$ .