1. Introduction to Electricity

• Definition: Electricity is a fundamental form of energy resulting from the existence and flow of electric charge.
• Electric Charge: An intrinsic property of matter.
  • Types: Positive (protons) and Negative (electrons).
  • Unit: Coulomb (C).
  • Fundamental Charge: The charge of a single electron or proton, e≈1.602×10−19 C.
  • Quantization of Charge: Electric charge exists in discrete packets; any charge (Q) is an integral multiple of the fundamental charge (Q=ne, where n is an integer).
  • Conservation of Charge: Total electric charge in an isolated system remains constant.
• Conductors: Materials that allow electric charge (electrons) to flow easily through them (e.g., metals like copper, silver, aluminum; graphite; human body; electrolytes).
• Insulators: Materials that resist the flow of electric charge (e.g., rubber, glass, plastic, wood, air).
• Semiconductors: Materials with conductivity between that of conductors and insulators (e.g., silicon, germanium). Their conductivity can be controlled.

2. Electrostatics (Charges at Rest)

• Coulomb’s Law: Describes the force between two point charges.
  • Statement: The electrostatic force between two point charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them. It acts along the line joining the charges.
  • Formula: F=kr2∣q1​q2​∣​
    • F: Electrostatic force.
    • q1​,q2​: Magnitudes of the charges.
    • r: Distance between the charges.
    • k: Coulomb’s constant, k=4πϵ0​1​≈9×109 N⋅m2/C2.
    • ϵ0​: Permittivity of free space (8.854×10−12 C2/N⋅m2).
  • Nature of Force: Repulsive for like charges, attractive for unlike charges.
• Electric Field (E): A region around an electric charge where another charge would experience an electrostatic force.
  • Definition: Force per unit positive test charge.
  • Formula: E=q0​F​ or for a point charge q: E=kr2∣q∣​
  • Unit: Newton per Coulomb (N/C) or Volt per meter (V/m).
  • Electric Field Lines: Visual representation of electric fields.
    • Originate from positive charges, terminate on negative charges.
    • Never cross each other.
    • Closer lines indicate a stronger field.
• Electric Potential (V): The amount of work done per unit positive test charge to bring it from infinity to a point in an electric field.
  • Scalar Quantity.
  • Formula (for a point charge q): V=krq​
  • Unit: Volt (V). (1 V=1 J/C)
• Electric Potential Difference (ΔV or pd): The work done per unit charge to move a charge between two points in an electric field.
  • ΔV=VB​−VA​=q0​WAB​​
  • This is what drives current in circuits.
• Capacitance (C): The ability of a conductor to store electric charge.
  • Formula: C=VQ​
    • Q: Charge stored.
    • V: Potential difference across the conductor.
  • Unit: Farad (F). (1 F=1 C/V)
  • Capacitor: A device designed to store electric charge and energy.
    • Consists of two conducting plates separated by a dielectric (insulating material).
    • Energy Stored: E=21​CV2=21​CQ2​=21​QV
  • Combinations of Capacitors:
    • Series: Ceq​1​=C1​1​+C2​1​+… (Charge is same, Voltage divides)
    • Parallel: Ceq​=C1​+C2​+… (Voltage is same, Charge divides)

3. Current Electricity (Charges in Motion)

• Electric Current (I): The rate of flow of electric charge.
  • Formula: I=tQ​
    • Q: Charge flowing.
    • t: Time taken.
  • Unit: Ampere (A). (1 A=1 C/s)
  • Conventional Current: Direction of flow of positive charge (opposite to electron flow).
• Ohm’s Law: Relates current, voltage, and resistance in a circuit.
  • Statement: The current flowing through a conductor is directly proportional to the potential difference across its ends, provided the physical conditions (like temperature) remain constant.
  • Formula: V=IR
    • V: Potential difference (voltage).
    • I: Current.
    • R: Resistance.
• Resistance (R): The opposition offered by a conductor to the flow of electric current.
  • Unit: Ohm (Ω).
  • Factors Affecting Resistance:
    • Length (L): R∝L
    • Area of Cross-section (A): R∝1/A
    • Nature of Material: Different materials have different resistivities.
    • Temperature: For most conductors, resistance increases with temperature.
  • Resistivity (ρ): An intrinsic property of a material, representing its resistance per unit length and unit cross-sectional area.
    • Formula: R=ρAL​
    • Unit: Ohm-meter (Ω⋅m).
  • Conductance (G): Reciprocal of resistance (G=1/R). Unit: Siemens (S).
  • Conductivity (σ): Reciprocal of resistivity (σ=1/ρ). Unit: Siemens per meter (S/m).
• Combinations of Resistors:
  • Series: Resistors connected end-to-end.
    • Req​=R1​+R2​+R3​+… (Current is same, Voltage divides)
  • Parallel: Resistors connected across the same two points.
    • Req​1​=R1​1​+R2​1​+R3​1​+… (Voltage is same, Current divides)
• Electric Power (P): The rate at which electrical energy is consumed or produced in a circuit.
  • Formula: P=VI=I2R=RV2​
  • Unit: Watt (W).
• Electric Energy: The total amount of electrical work done or energy consumed over a period of time.
  • Formula: E=Pt=VIt=I2Rt=RV2​t
  • Unit: Joule (J).
  • Commercial Unit: Kilowatt-hour (kWh). (1 kWh=3.6×106 J).

4. Heating Effects of Electric Current (Joule Heating)

• Joule’s Law of Heating: When current flows through a resistor, electrical energy is converted into heat.
  • Formula: H=I2Rt
    • H: Heat produced.
    • I: Current.
    • R: Resistance.
    • t: Time.
• Applications: Electric heaters, geysers, toasters, electric irons, incandescent light bulbs (though inefficient for light), fuses.

5. Magnetic Effects of Electric Current

• Oersted’s Discovery: An electric current produces a magnetic field around it.
• Electromagnetism: The study of the relationship between electricity and magnetism.
• Magnetic Field: A region around a magnet or a current-carrying conductor where magnetic forces can be observed.
  • Unit: Tesla (T) or Gauss (G). (1 T=104 G)
• Magnetic Field Lines:
  • Originate from the North pole and end at the South pole outside the magnet.
  • Form continuous closed loops (inside the magnet, they go from South to North).
  • Never cross each other.
  • Closer lines indicate a stronger field.
• Force on a Current-Carrying Conductor in a Magnetic Field:
  • Formula: F=I(L×B) or F=BILsinθ
    • Fleming’s Left-Hand Rule: Used to determine the direction of force, magnetic field, and current.
  • Applications: Electric motors, galvanometers, loudspeakers.
• Force between Two Parallel Current-Carrying Conductors:
  • Attractive if currents are in the same direction.
  • Repulsive if currents are in opposite directions.
• Solenoid: A coil of wire wound into a tightly packed helix.
  • Produces a strong and uniform magnetic field inside when current passes through it.
  • Behaves like a bar magnet.
• Electromagnet: A temporary magnet created by passing electric current through a coil of wire, often wound around a ferromagnetic core.
  • Strength can be varied by changing current or number of turns.
  • Applications: Cranes, doorbells, circuit breakers, relays.

6. Electromagnetic Induction (EMI)

• Faraday’s Laws of Electromagnetic Induction:
  • First Law: Whenever the magnetic flux linked with a coil changes, an electromotive force (EMF) is induced in the coil.
  • Second Law: The magnitude of the induced EMF is directly proportional to the rate of change of magnetic flux linked with the coil.
    • Formula: E=−NdtdΦB​​
      • E: Induced EMF.
      • N: Number of turns in the coil.
      • ΦB​: Magnetic flux (BAcosθ).
      • Negative sign is due to Lenz’s Law.
• Lenz’s Law: The direction of the induced current is such that it opposes the cause that produced it.
  • A consequence of the conservation of energy.
• Motional EMF: EMF induced when a conductor moves through a magnetic field.
  • Formula: E=BLvsinθ
    • B: Magnetic field strength.
    • L: Length of the conductor.
    • v: Velocity of the conductor.
• Applications:
  • Generators (Dynamos): Convert mechanical energy into electrical energy using EMI.
    • AC Generators: Produce alternating current.
    • DC Generators: Produce direct current.
  • Transformers: Devices that change AC voltage levels (step-up or step-down) based on EMI.
    • Work only with AC.
    • Step-up Transformer: Increases voltage, decreases current.
    • Step-down Transformer: Decreases voltage, increases current.
  • Induction Cooktops: Use induced eddy currents for heating.
  • Metal Detectors.

7. Alternating Current (AC) vs. Direct Current (DC)

• Direct Current (DC):
  • Electric charge flows in only one constant direction.
  • Produced by batteries, solar cells, DC generators.
  • Applications: Electronic devices, LED lights, electric vehicles.
• Alternating Current (AC):
  • Electric charge periodically reverses direction.
  • Produced by AC generators (alternators).
  • Advantages:
    • Can be easily transformed to different voltage levels using transformers, making long-distance transmission more efficient (reduced power loss due to heating).
    • Easier to generate.
  • Applications: Household electricity, industrial power, power grids.

8. Household Electric Circuits

• Wiring System: Typically uses three types of wires:
  • Live Wire (Phase Wire): Carries current from the power station (usually red or brown).
  • Neutral Wire: Completes the circuit, returning current to the power station (usually black or light blue).
  • Earth Wire: A safety wire connected to the metallic casing of appliances to prevent electric shock in case of insulation failure (usually green).
• Circuit Protection Devices:
  • Fuses: Short piece of wire that melts and breaks the circuit if current exceeds a safe limit.
  • Miniature Circuit Breakers (MCBs): Automatic switches that trip and break the circuit when current exceeds a safe limit, and can be reset.
  • Residual Current Devices (RCDs) / Earth Leakage Circuit Breakers (ELCBs): Detect current imbalances (leakage to earth) and quickly trip to prevent electric shock.
• Common Hazards:
  • Overloading: Too many appliances connected to one circuit, drawing excessive current.
  • Short Circuiting: Live and neutral wires come into direct contact, leading to very low resistance and very high current.
  • Electric Shock: Current passing through the human body.

9. Other Key Concepts & Applications

• Electrolysis: Chemical changes brought about by passing electric current through an electrolyte.
• Thermoelectricity: Production of electric current from temperature differences (Seebeck effect) or vice versa (Peltier effect).
• Photovoltaic Effect: Conversion of light energy into electrical energy (e.g., solar cells).
• Piezoelectric Effect: Production of electricity from mechanical stress or vice versa.