CIE IGCSE Physics: Electrical Quantities Comprehensive Study Notes

Electric Charge, Atoms, and Forces

  • Types of Charge: There are two types of electric charge: positive (++) and negative (−-).

  • Atomic Structure:

    • Electrons: Negatively charged particles found inside the atom.

    • Protons: Positively charged particles found inside the atom.

    • Neutrons: Neutral particles (no charge) found inside the atom.

  • Electrical Neutrality: Atoms contain equal numbers of protons and electrons. Because their charges are equal and opposite, they cancel out, resulting in an overall charge of zero.

  • Attraction and Repulsion (Electrostatic Forces):

    • Objects with opposite charges (positive and negative) attract each other (move closer together).

    • Objects with like charges (positive and positive, or negative and negative) repel each other (move further apart).

    • Summary Table:

    • Positive + Positive = Repel

    • Positive + Negative = Attract

    • Negative + Positive = Attract

    • Negative + Negative = Repel

  • Unit of Charge: Electric charge is measured in coulombs (CC).

Demonstrating Electric Charges by Friction

  • Charging by Friction: When specific insulating solids are rubbed together, electrons are transferred from one material to the other.

    • The material that gains electrons becomes negatively charged.

    • The material that loses electrons becomes positively charged.

    • Note: Only electrons are transferred; positive charges do not move during friction.

  • Examples of Charging:

    • Polythene Rod: Rubbing an uncharged polythene rod with an uncharged cloth causes electrons to move from the cloth to the rod. The rod becomes negatively charged, and the cloth becomes positively charged.

    • Acetate Plastic Rod: Rubbing an uncharged acetate rod with an uncharged cloth causes electrons to move from the rod to the cloth. The rod becomes positively charged, and the cloth becomes negatively charged.

  • Experimental Investigation of Friction:

    • Aim: To observe how insulating materials charge via friction.

    • Method: Rub a polythene rod and suspend it in a cradle. Bring a second charged rod (e.g., another polythene rod or an acetate rod) close to it to observe attraction or repulsion.

    • Safety/Precision Tips: Avoid touching the charged ends (as they will discharge) and minimize environmental factors like drafts.

  • Detecting Charge with a Gold-Leaf Electroscope:

    • Setup: Consists of a metal plate, a metal stem, and a thin gold leaf housed in an airtight container.

    • Mechanism (Near Plate): Bringing a negatively charged rod near the plate repels electrons down to the leaf and stem, causing them both to become negative and repel (leaf rises). A positive rod attracts electrons to the plate, leaving the leaf and stem positive (leaf rises).

    • Mechanism (Touching Plate): Touching the plate transfers charge; the leaf stays risen until discharged.

    • Discharging (Earthing): Touching the plate with a finger allows charge to flow to the earth, returning the electroscope to a neutral state (leaf falls).

Electric Fields

  • Definition: An electric field is a region of space in which an electric charge experiences a force.

  • Direction of Field: Defined as the direction of the force on a positive charge at that point.

  • Properties: Electric fields are vector quantities (having magnitude and direction).

  • Field Patterns:

    • Positive Point Charge: Field lines are directed radially outwards.

    • Negative Point Charge: Field lines are directed radially inwards.

    • Charged Conducting Sphere: Field lines are radial (similar to a point charge) and perpendicular (90∘90^\circ) to the surface. Charges distribute evenly across the surface due to mutual repulsion.

    • Parallel Plates: The field between two oppositely charged parallel plates is uniform. The field lines are parallel, straight, equally spaced, and directed from the positive plate to the negative plate.

Electrical Conductors and Insulators

  • Conductors: Materials that allow charge (electrons) to flow easily.

    • Examples: Silver, copper, aluminium, steel, and graphite (a non-metal).

    • Metallic Structure: Metals contain a lattice of positive metal ions surrounded by a "sea" of delocalised electrons that are free to move.

  • Insulators: Materials that do not have free charges and do not allow charge to flow easily.

    • Examples: Rubber, plastic, glass, wood.

    • Note: Some insulators (like wood) can conduct small amounts of static electricity but are still categorized as poor conductors.

  • Testing Conductivity Experiment:

    • Use a charged gold-leaf electroscope. Touch the metal plate with the test material.

    • Good Conductor: The leaf falls quickly as charge flows away.

    • Poor Conductor/Insulator: The leaf falls slowly or not at all.

Electric Current

  • Definition: The rate of flow of electric charge (QQ) per unit time (tt).

  • Formula: I=QtI = \frac{Q}{t}

    • I=Current in Amperes (A)I = \text{Current in Amperes (A)}

    • Q=Charge in Coulombs (C)Q = \text{Charge in Coulombs (C)}

    • t=Time in seconds (s)t = \text{Time in seconds (s)}

  • Equivalence: 1 A=1 C/s1\,A = 1\,C/s.

  • Conduction in Metals: Current in a wire is the flow of negatively charged electrons through the metal lattice.

  • Conventional Current vs. Electron Flow:

    • Conventional Current: Defined as the flow of positive charge from the positive (++) terminal to the negative (−-) terminal.

    • Electron Flow: Electrons, being negative, actually flow from the negative (−-) terminal to the positive (++) terminal.

  • Measuring Current: Use an ammeter connected in series. Ammeters can be analogue (prone to parallax error) or digital (more precise but may flicker).

Direct and Alternating Current

  • Direct Current (d.c.): A steady current flowing in only one direction (positive to negative). Produced by cells and batteries.

  • Alternating Current (a.c.): A current that continuously changes direction, moving back and forth. Produced by electrical generators and used in mains supply.

  • UK Mains Electricity: Frequency of 50 Hz50\,Hz (changes direction 50 times per second) and potential difference of approximately 230 V230\,V.

Electromotive Force (e.m.f.) and Potential Difference (p.d.)

  • Electromotive Force (e.m.f.): The name for the potential difference of a power source. It is the electrical work done by a source in moving a unit charge around a complete circuit.

  • Potential Difference (p.d.): The work done (WW) by a unit charge passing through a component. It represents the energy transferred between two points.

  • Formula: V=WQV = \frac{W}{Q} (or E=WQE = \frac{W}{Q} for e.m.f.)

    • V=Potential Difference (V)V = \text{Potential Difference (V)}

    • W=Energy Transferred or Work Done (J)W = \text{Energy Transferred or Work Done (J)}

    • Q=Charge (C)Q = \text{Charge (C)}

  • Unit: Volt (VV), where 1 V=1 J/C1\,V = 1\,J/C.

  • Measuring p.d.: Use a voltmeter connected in parallel across the component.

Resistance

  • Definition: The opposition to current flow. It is caused by collisions between free electrons and the metal ions in a wire.

  • Ohm's Law: Resistance (RR) is the ratio of potential difference (VV) to current (II).

  • Formula: R=VIR = \frac{V}{I}

    • R = \text{Resistance in Ohms (\Omega)}

    • V=p.d. in Volts (V)V = \text{p.d. in Volts (V)}

    • I=Current in Amps (A)I = \text{Current in Amps (A)}

  • Relationship: Current and resistance are inversely proportional (doubling resistance halves current for a constant p.d.).

  • Current-Voltage (I-V) Graphs:

    • Ohmic Conductors (Fixed Resistors/Wires): Straight line through the origin. Resistance is constant.

    • Filament Lamps (Non-Ohmic): S-shaped curve. As current increases, the temperature of the filament rises, causing metal ions to vibrate more, which increases resistance.

    • Diodes: Allows current in one direction only (Forward Bias). In Reverse Bias, resistance is extremely high, and no current flows.

Resistance of a Wire

  • Length (LL): Resistance is directly proportional to length (R∝LR \propto L). Longer wires have more metal ions for electrons to collide with.

  • Cross-Sectional Area (AA): Resistance is inversely proportional to cross-sectional area (R∝1AR \propto \frac{1}{A}). Thicker wires provide more pathways for electrons, reducing resistance.

Electrical Energy and Power

  • Energy Transfer: Energy is transferred from the power supply (chemical or mains) to components (kinetic for motors, thermal for heaters).

  • Electrical Energy Equation: E=V×I×tE = V \times I \times t

    • E=Energy (J)E = \text{Energy (J)}

    • V=p.d. (V)V = \text{p.d. (V)}

    • I=Current (A)I = \text{Current (A)}

    • t=Time (s)t = \text{Time (s)}

  • Electrical Power (PP): The rate at which energy is transferred.

    • Formulas:

    • P=Et=WtP = \frac{E}{t} = \frac{W}{t}

    • P=I×VP = I \times V

    • Unit: Watt (WW), where 1 W=1 J/s1\,W = 1\,J/s.

  • Kilowatt-hour (kW hkW\,h): A unit of energy used for billing in homes and businesses.

    • Definition: Energy transferred by a 1 kW1\,kW appliance running for 1 hour1\,hour.

    • Conversions:

    • 1 kW h=1000 W×3600 s=3.6×106 J1\,kW\,h = 1000\,W \times 3600\,s = 3.6 \times 10^6\,J

    • To convert kW hkW\,h to Joules: Multiply by 3.6×1063.6 \times 10^6.

    • To convert Joules to kW hkW\,h: Divide by 3.6×1063.6 \times 10^6.

  • Cost Calculation: Cost=Energy in kW h×Price per kW h\text{Cost} = \text{Energy in } kW\,h \times \text{Price per } kW\,h.