1. Electromagnetic Induction

-Motional EMF:

• Concept:

  • When a conductor moves through a magnetic field, it induces an electromotive force (EMF).

• Physics:

  • Free electrons in the conductor experience a force due to the magnetic field, leading to a separation of charges and an electric field within the conductor.

• Formula:

  • The induced EMF (ε) is given by ε=BvL, where

    • B is the magnetic field strength,

    • v is the velocity of the conductor, and

    • L is the length of the conductor perpendicular to the direction of motion.

• Equilibrium:

  • The induced EMF continues until the electric force from the built-up charge balances the magnetic force, eε=evB.

-Magnetic Flux and Faraday’s Law

• Magnetic Flux (Φ): Quantified as representing the total magnetic field moving through an area A at angle

• Faraday’s Law: The induced EMF in a circuit is equal to the negative rate of change of magnetic flux through the circuit

-Lenz’s Law:

• The direction of the induced EMF and current is such that it opposes the change in magnetic flux that produced it, conserving energy.

• Demonstrated by considering the direction of force on electrons due to the magnetic field and the resulting direction of current flow.

• Applications and Implications

  • Lenz’s and Faraday’s laws are foundational for the functioning of electrical generators, transformers, and induction-based technologies.

  • The laws also provide a deeper understanding of the interplay between electricity and magnetism, showcasing the principle that changing magnetic fields can induce electrical currents.

-Transmission of Power

• Alternating Current (AC)

  • AC is produced by an AC generator, where a coil rotating in a magnetic field induces an EMF due to electromagnetic induction.

  • AC changes direction periodically, with the EMF and current represented as sinusoidal functions over time.

• The AC Generator

  • Converts mechanical energy into electrical energy using electromagnetic induction.

  • A coil rotates within a magnetic field, cutting through magnetic field lines, thus inducing an EMF and current.

  • The EMF (ε) Induced in the coil is proportional to the rate of change of magnetic flux, given by

    • ε=N(dΦ/dt)

      • N is the number of turns in the coil.

-Root Mean Square (RMS) Quantities

• RMS values provide a measure of the equivalent steady DC values that would produce the same power.​

• peak voltage and current respectively, divided by root 2, gives the respective rms values.

• RMS values are used because power in an AC circuit depends on these average values rather than the peak values.

• The Transformer:

  • A device that changes the voltage level of AC without changing its frequency through electromagnetic induction.

  • Consists of primary and secondary coils around a core, with the voltage change ratio determined by the ratio of turns in the coils

  • Power loss in transformers occurs mainly due to eddy currents, which are minimized by laminating the core, and magnetic hysteresis.

• Transformers and Power Transmission:

  • Step-up transformers increase voltage, reducing current for efficient long-distance power transmission, minimising power loss (P=I²R)

  • Step-down transformers reduce voltage to safe levels for domestic and industrial use.

  • Power plants use high voltages to transmit power over long distances to reduce energy loss.

Diode Bridges and Rectification

• Diode bridges convert AC to direct current (DC).

  • Half-wave rectification uses a single diode to allow current in only one direction, resulting in a loss of half the waveform.

  • Full-wave rectification uses a bridge rectifier to use both halves of the AC waveform, improving efficiency.

  • During one half-cycle, two diodes conduct, allowing current flow in one direction; during the opposite half-cycle, the other two diodes conduct, maintaining the direction of current flow.

2. Capacitance

• Definition and Basic Concept:

  • Capacitance (C): The ability of a system to store charge per unit voltage, defined as C, where

    • q is the charge

    • V is the potential difference

    • Unit of capacitance is the farad (F), where 1 F = 1 C/V.

  • Capacitance of a Parallel Plate Capacitor

    • Depends on the geometry: where

      • d is the distance between plates

      • is the permittivity of the medium

      • A is the plate area.

• Effect of Dielectric on Capacitance

  • Inserting a dielectric material between the plates of a capacitor increases its capacitance by reducing the electric field, which allows the capacitor to store more charge for the same voltage.

  • Capacitors in Parallel and Series

    • Parallel Configuration:

      • Capacitances add up ( C_total = C₁₊C₂₊C_3…….)

    • Series Configuration:

      • Inverses of capacitances add up.

• Energy Stored in a Capacitor

  • Represents the work done to charge the capacitor.

  • Charging and Discharging a Capacitor

    • Charging: When connected to a voltage source, the capacitor charges up following an exponential curve, approaching its maximum charge asymptotically.

    • Discharging: The stored energy in the capacitor is released when the circuit is closed, discharging exponentially to zero.

  • Capacitors in Rectification

    • Used in conjunction with diodes in power supply circuits to smooth the output from rectifiers.

    • During the half-cycle when the AC is in the correct direction, the capacitor charges up, and during the opposite half-cycle, it discharges, providing a more continuous DC output.