Electricity

1.1 Electrical Quantities

• Electric Charge (Q)

  • The property of matter that causes it to experience a force when placed in an electric field.

  • Unit: Coulombs (C)

  • Example: A charge of 1 C is equal to the charge of approximately 6.242×10¹⁸ electrons.

• Current (I)

  • Definition: The rate of flow of charge.

  • Unit: Amperes (A)

  • Formula: I = Q/t  

  • Example: A current of 2 A means 2 C of charge passes a point in the circuit every second.

  • In metals, current is the flow of electrons.

• Voltage (V)

  • The potential difference between two points; the work done to move a unit charge between those points.

  • Unit: Volts (V)

  • Formula: V = W/Q  

  • Potential difference (voltage) is the energy transferred per unit charge passed. Thus, one volt is equivalent to one joule per coulomb.

  • Example: A battery that provides 9 V does 9 joules of work per coulomb of charge.

• Resistance (R)

  • The opposition to the flow of electric current.

  • Unit: Ohms (Ω)

  • Formula: R = V/I 

  • Example: If a resistor has a voltage of 10 V across it and a current of 2 A flowing through it, its resistance is 5 Ω.

  • Changing Resistance: Using a variable resistor in a circuit can change the resistance, thereby changing the current.

• Charge (Q)

  • Formula: Q = I × t 

  • Explanation: Charge (Coulomb, C) is the product of current (Ampere, A) and time (second, s).

1.2 Ohm's Law

• Statement: The current through a conductor between two points is directly proportional to the voltage across the two points, provided the temperature remains constant.

• Formula: V = IR 

• Graph: A linear graph showing direct proportionality between current and voltage for a conductor obeying Ohm’s law.

1.3 Electrical Power

• The rate at which electrical energy is transferred by an electric circuit.

• Unit: Watts (W)

• Formulas:

  • P = IV

  • P = I²R

  • P = V²/R

• Example: A 60 W light bulb uses 60 joules of energy per second.

1.4 Energy Transfer

• Formula: E = IVt 

• Explanation: Energy transferred (Joule, J) is the product of current (Ampere, A), potential difference (Volt, V), and time (second, s).

1.5 Power

• Definition: The rate of energy transfer.

• Unit: Watts (W)

• Formula: Power(W) = Energy transferred (J)/Time(s) ​

Circuits

2.1 Series and Parallel Circuits

Series Circuits

• Characteristics

  • Current: Same through all components.

  • Voltage: Sum of voltages across components equals total voltage.

  • Resistance: Rₜₒₜₐₗ = R₁ + R₂ +…  

  • Explanation: If two resistors are in series, the net resistance is increased.

• Example: Christmas lights where one bulb failure affects the entire string.

Parallel Circuits

• Characteristics

  • Current: Sum of currents through each path equals total current.

  • Voltage: Same across each component.

  • Resistance: 1/Rₜₒₜₐₗ = (1/R₁) + (1R₂) +... 

  • Explanation: If two resistors are in parallel, the net resistance is decreased.

  • Example: Household electrical wiring.

2.2 Circuit Components

• Symbols and Functions

  • Battery: Provides electrical energy.

  • Resistor: Limits current flow.

  • Ammeter: Measures current (connected in series).

  • Voltmeter: Measures voltage (connected in parallel).

  • Switch: Opens and closes the circuit.

• Closed Circuit: A complete circuit where current can flow uninterrupted.

2.3 Kirchhoff's Laws

• Kirchhoff's Current Law (KCL): Total current entering a junction equals the total current leaving.

• Kirchhoff's Voltage Law (KVL): Total voltage around a closed loop equals zero.

2.4 Device Behavior in Circuits

• Filament Lamps: The resistance increases as the temperature of the filament increases.

• Diodes: Allow current to flow in one direction only, with very high resistance in the reverse direction.

• Fixed Resistors: Have a constant resistance regardless of the voltage and current.

2.5 Variable Resistances

• Light-Dependent Resistor (LDR): Resistance decreases as light intensity increases.

• Thermistors: Resistance decreases as temperature increases.

• Exploring Variation: Use of circuits to investigate how resistance changes in filament lamps, diodes, thermistors, and LDRs.

Electromagnetism

3.1 Magnetic Fields

• Magnetic Field Lines: Represent the direction and strength of the magnetic field. They flow from the north to the south pole of a magnet.

• Magnetic Flux (Φ): The total magnetic field passing through a given area.

3.2 Electromagnets

• Definition: Magnets created by electric current flowing through coils of wire.

• Applications: Used in motors, generators, transformers, and relays.

• Construction: Typically a coil of wire (solenoid) with a ferromagnetic core.

3.3 The Motor Effect

• Definition: A current-carrying conductor in a magnetic field experiences a force.

• Fleming's Left-Hand Rule: Used to determine the direction of force on a current-carrying conductor.

  • Thumb: Force (F)

  • First Finger: Magnetic Field (B)

  • Second Finger: Current (I)

  • Formula: F = BIL 

  • Example: Electric motors use this effect to produce motion.

3.4 Electromagnetic Induction

• Faraday’s Law: Induced voltage in a circuit is proportional to the rate of change of magnetic flux through the circuit.

• Lenz’s Law: The direction of the induced current opposes the change in magnetic flux.

• Formula: Induced Voltage = −dΦ/dt 

• Applications: Transformers and electric generators operate based on this principle.

3.5 Transformers

• Definition: Devices that transfer electrical energy between two or more circuits through electromagnetic induction.

• Principle: Operates on AC; changing current in the primary coil induces a current in the secondary coil.

• Formula: VₚVₛ = NₚNₛ  

• Efficiency: Ideal transformers assume 100% efficiency (no energy loss).

Electrical Energy and Safety

4.1 Energy Dissipation

• Thermal Energy: Electrical energy is dissipated as thermal energy in the surroundings when an electric current does work against electrical resistance.

• Reducing Unwanted Energy Transfer: Use low resistance wires to minimize energy loss.

4.2 Heating Effect of Current

• Advantages: Useful in devices like electric heaters and toasters.

• Disadvantages: Unwanted heating can damage components and reduce efficiency.

4.3 Power and Energy Transfer

• Equation: E = IVt 

• Power Formula:

  • Power(W) = Energy transferred (J) ​/ Time(s)

  • P= IV

  • P = I²R 

4.4 Domestic Electrical Systems

• Energy Transfer: Batteries and the a.c. mains supply energy to motors and heating devices.

• Direct vs Alternating Voltage:

  • Direct Current (DC): Charge flows in one direction; supplied by cells and batteries.

  • Alternating Current (AC): Charge flow direction alternates; supplied by mains electricity.

• Wiring:

  • Live Wire: Carries current to the appliance.

  • Neutral Wire: Completes the circuit.

  • Earth Wire: Safety wire to prevent electric shocks

• Safety:

  • Fuses and Circuit Breakers: Protect circuits from excessive current.

  • Switches and Fuses Location