Electricity & Magnetism

Section 1: Electric Circuits

This section covers the fundamental principles governing the flow of electricity in circuits.

1.1 Fundamental Quantities

* Electric Charge (Q): A fundamental property of matter. The smallest unit of charge is that of an electron. The SI unit for charge is the coulomb (C).

* Electric Current (I): The rate of flow of electric charge. It is defined by the equation I = Q/t, where Q is the charge in coulombs and t is the time in seconds. The SI unit for current is the ampere (A). A current of 1A means 1 coulomb of charge is flowing past a point every second.

* Voltage (V): Also known as potential difference, it is the work done or energy transferred per unit charge. It's the 'push' that drives the current. Defined as V = E/Q, where E is the energy in joules. The SI unit is the volt (V).

* Resistance (R): The opposition to the flow of current. A component has a resistance of 1 ohm if a voltage of 1 volt drives a current of 1 ampere through it. The SI unit is the ohm (Ω).

1.2 Ohm's Law and I-V Characteristics

Ohm's Law states that for an ohmic conductor at a constant temperature, the current is directly proportional to the voltage across it. This gives the famous equation:

V = I × R

* Common Misconception: Ohm's Law is not universal. It only applies to ohmic conductors (like a standard resistor). Many components are non-ohmic.

Current-Voltage (I-V) Graphs:

1. Fixed Resistor (Ohmic): A straight line through the origin, indicating that resistance is constant.
2. Filament Lamp (Non-Ohmic): The graph is an 'S'-shaped curve. As voltage increases, the filament gets hotter, its resistance increases, so the current increases at a slower rate.
3. Diode (Non-Ohmic): Allows current to flow easily in one direction (forward bias) but has very high resistance in the opposite direction (reverse bias). The graph is almost flat on the negative voltage axis and rises sharply after a small positive voltage.

1.3 Series and Parallel Circuits

* Series Circuits: Components are connected end-to-end.

* Current: is the same through all components (I_total = I₁ = I₂ = ...).

* Voltage: The total voltage from the supply is shared between components (V_total = V₁ + V₂ + ...).

* Resistance: The total resistance is the sum of individual resistances (R_total = R₁ + R₂ + ...).

* Parallel Circuits: Components are connected in separate branches.

* Current: The total current from the supply splits between the branches (I_total = I₁ + I₂ + ...).

* Voltage: is the same across all branches (V_total = V₁ = V₂ = ...).

* Resistance: The reciprocal of the total resistance is the sum of the reciprocals of individual resistances (1/R_total = 1/R₁ + 1/R₂ + ...). The total resistance is always less than the smallest individual resistor.

* Practical Application: Household wiring in Pakistan (e.g., in Lahore or Islamabad) is in parallel. This ensures every appliance receives the full ~230V mains supply and can be switched on/off independently.

1.4 Electrical Power and Energy

* Power (P): The rate at which energy is transferred. Measured in watts (W).

* P = I × V (Power = Current × Voltage)

* Using V=IR, we can also derive: P = I²R and P = V²/R.

* Energy (E): The total energy transferred over a period of time. Measured in joules (J).

* E = P × t (Energy = Power × time)

* This is the basis for electricity bills from providers like K-Electric, which are calculated in kilowatt-hours (kWh), a unit of energy (1 kWh = 3.6 million Joules).

Section 2: Magnetism and Electromagnetism

This section explores the relationship between electricity and magnetism, which is the foundation for motors and generators.

2.1 Magnetism

* Permanent Magnets: Have a north pole (N) and a south pole (S). Like poles repel; unlike poles attract.

* Magnetic Field: A region where a magnetic material experiences a force. Field lines are used to represent it, always pointing from North to South.

2.2 Electromagnetism

* A current flowing through a wire creates a magnetic field around it.

* Right-Hand Grip Rule: To find the direction of the magnetic field around a straight wire or the North pole of a coil:

* Point your right thumb in the direction of the conventional current.

* Your fingers will curl in the direction of the magnetic field lines.

* For a solenoid (a long coil), if your fingers curl in the direction of the current, your thumb points to the North pole.

* Electromagnets: A solenoid with a soft iron core. Its strength can be increased by:

1. Increasing the current.
2. Increasing the number of turns in the coil.
3. Inserting a soft iron core (which concentrates the magnetic field lines).

2.3 The Motor Effect and DC Motors

* The Motor Effect: A conductor carrying a current placed in a magnetic field will experience a force, provided the wire is not parallel to the field lines.

* Fleming's Left-Hand Rule: Used to predict the direction of the force (motion).

* ThuMb → Motion / Force

* First finger → Field (N to S)

* SeCond finger → Current (+ to -)

* Exam Trap: Do not confuse this with the Right-Hand (Generator) Rule.

* Simple DC Motor: Consists of a coil of wire in a magnetic field. To ensure continuous rotation, a split-ring commutator is used. Its function is to reverse the direction of the current in the coil every half-turn, which in turn reverses the direction of the forces on the sides of the coil, keeping it spinning in the same direction.

2.4 Electromagnetic Induction and Transformers

* Electromagnetic Induction: The process of generating a voltage (and a current, if there is a complete circuit) in a conductor by changing the magnetic field around it. This can be done by moving a wire through a magnetic field, or moving a magnet relative to a coil.

* Transformers: Devices that use electromagnetic induction to change the voltage of an alternating current (AC). They do not work with DC.

* Structure: Two coils, a primary coil and a secondary coil, are wrapped around a laminated soft iron core.

* Principle: An alternating current in the primary coil creates a continuously changing magnetic field in the iron core. This changing magnetic field induces an alternating voltage in the secondary coil.

* Transformer Equation: `Vp / Vs = Np / Ns`

* (Primary Voltage / Secondary Voltage = Primary Turns / Secondary Turns)

* Step-up Transformer: `Ns > Np`, so `Vs > Vp`. Increases voltage (used at power stations).

* Step-down Transformer: `Ns < Np`, so `Vs < Vp`. Decreases voltage (used in local substations and device chargers).