Equivalent Circuits - Example 4- Conical Resistor

Slide 1: Equivalent Circuits - Conical Resistor

Definition of a conical resistor
Structure and geometry of a conical resistor
Material properties and resistivity
Conical resistor in a circuit
Application examples of conical resistors

Slide 2: Structure and Geometry of a Conical Resistor

Description of the shape and structure of a conical resistor
Tapered or conical shape
Cross-sectional area variations along the length
Length and diameter measurements
Visual representation of a conical resistor

Slide 3: Material Properties and Resistivity

Introduction to electrical resistivity
Definition of resistivity and its unit
Different materials with varying resistivity values
Dependence of resistivity on temperature
Factors affecting resistivity in conical resistors

Slide 4: Conical Resistor in a Circuit

Demonstration of a conical resistor connected in a circuit
Placement of conical resistor within a circuit diagram
Interactions and behavior of conical resistor in the circuit
Voltage drops and current flow through the conical resistor
Impact of conical resistor on the overall circuit performance

Slide 5: Application Examples of Conical Resistors

Usage in heating systems and appliances
Control of current flow in electronic devices
Voltage regulation applications
Power dissipation in certain components
Use in electrical measurement devices

Slide 6: Magnetic Fields - Introduction

Definition and properties of magnetic fields
Magnetic field lines and their direction
Relationship between current and magnetic fields
Exploring the connection between electricity and magnetism
The magnetic field around a straight current-carrying wire

Slide 7: Magnetic Field Due to a Straight Wire

Calculation of magnetic field intensity using the Biot-Savart Law
Examples of magnetic field calculations for a straight wire
Determination of magnetic field direction using the right-hand rule
Magnetic field strength at different distances from the wire
Applications of the magnetic field due to straight wires

Slide 8: Magnetic Field Due to a Circular Loop

Calculation of magnetic field intensity at the center of a circular loop
Examples of magnetic field calculations for circular loops
Dependence of magnetic field on the loop radius and current
Magnetic field direction in and around the circular loop
Applications of the magnetic field due to circular loops

Slide 9: Magnetic Field Due to a Solenoid

Definition and structure of a solenoid
Magnetic field intensity inside a solenoid
Calculation of magnetic field strength using Ampere’s Law
Relationship between magnetic field and current in a solenoid
Applications of solenoids in various technologies

Slide 10: Electromagnetic Induction

Introduction to electromagnetic induction
Relationship between magnetic fields and electric currents
Explanation of Faraday’s law of electromagnetic induction
Calculation of induced electromotive force (emf)
Applications of electromagnetic induction in generators and transformers

Slide 11: Equivalent Circuits - Example 4: Conical Resistor

Problem statement: A conical resistor is connected to a power source with a current of 2A. The resistor has a length of 10cm and a diameter of 5cm at its wider end. The resistivity of the material is given as 1.5 x 10^-6 Ω.m. Calculate the resistance of the conical resistor.
Calculating the cross-sectional area at the wider end using the formula: A = πr^2
Calculating the cross-sectional area at the narrower end using the formula: A = πr^2
Determining the resistance using the formula: R = ρ * (L / A)
Substituting the values and solving for resistance
The resistance of the conical resistor is obtained as the result.

Slide 12: Induced Current and Magnetic Fields

Introduction to induced current in a circuit
Explanation of Faraday’s law of electromagnetic induction
Relationship between magnetic fields and induced current
Calculation of induced current using the formula: emf = -dΦ/dt
Direction of induced current using Lenz’s law
Examples of induced current in different scenarios

Slide 13: Self-Inductance

Definition of self-inductance in a circuit
Concept of magnetic flux linkage and mutual inductance
Relationship between self-inductance and induced emf
Calculation of self-inductance using the formula: L = Φ/I
Determining the unit of self-inductance (H)
Applications of self-inductance in coils and transformers

Slide 14: Mutual Inductance

Introduction to mutual inductance between two coils
Explanation of coupling coefficient and shared magnetic flux
Relationship between mutual inductance and induced emf in the secondary coil
Calculation of mutual inductance using the formula: M = Φ₂ / I₁
Determining the unit of mutual inductance (H)
Applications of mutual inductance in transformers and inductive sensors

Slide 15: Equivalent Circuits - Example 5: Inductor

Problem statement: A circuit has an inductor with an inductance value of 2H connected in series with a resistance of 5Ω. The circuit is powered by a 12V battery. Calculate the current flowing through the circuit.
Analysis of the circuit using Kirchhoff’s laws
Writing the equation using Ohm’s law: V = IR
Writing the equation using the inductor’s voltage-current relationship: V = L (dI / dt)
Combining the two equations and solving for current
The current flowing through the circuit is obtained as the result.

Slide 16: Phase Difference and Power Factor

Explanation of phase difference between voltage and current in AC circuits
Calculation of phase angle using trigonometry: cos θ = P / S
Definition of power factor and its significance
Calculation of power factor using the formula: PF = cos θ
Interpretation of different power factor values
Examples of power factor and its impact on electrical systems

Slide 17: Capacitors - Introduction

Definition and structure of a capacitor
Functioning of a capacitor in a circuit
Analysis of the capacitor charging and discharging processes
Capacitance and its unit (Farad)
Types of capacitors and their applications
Symbol representation of capacitors in circuit diagrams

Slide 18: Capacitance and Energy Stored

Definition and calculation of capacitance using the formula: C = Q / V
Dependence of capacitance on physical factors
Calculation of energy stored in a capacitor using the formula: E = (1/2)CV^2
Examples of calculating capacitance and energy stored
Applications of capacitors in energy storage and signal filtering
Safe handling and precautionary measures with capacitors

Slide 19: Equivalent Circuits - Example 6: Capacitor

Problem statement: A circuit consists of a capacitor with a capacitance of 300μF connected in parallel with a resistor of 2kΩ. The circuit is connected to a 6V battery. Calculate the charge stored in the capacitor.
Analysis of the circuit using Kirchhoff’s laws
Calculation of voltage across the resistor using Ohm’s law: V = IR
Calculation of voltage across the capacitor using the battery voltage
Calculation of charge stored in the capacitor using the formula: Q = C * V
Substituting the values and solving for charge
The charge stored in the capacitor is obtained as the result.

Slide 20: Magnetic Flux and Flux Density

Definition of magnetic flux and its unit (Weber)
Calculation of magnetic flux using the formula: Φ = B * A
Explanation of flux density and its unit (Tesla)
Calculation of flux density using the formula: B = Φ / A
Relationship between magnetic field strength and flux density
Examples of magnetic flux and flux density calculations.

Slide 21: Magnetic Forces

Introduction to magnetic forces
Definition of magnetic force on a current-carrying wire
Calculation of magnetic force using the formula: F = BILsinθ
Relationship between magnetic field, current, length, and angle
Examples of magnetic force calculations
Applications of magnetic forces in motors and generators

Slide 22: Magnetic Torque

Definition of magnetic torque on a current loop
Calculation of magnetic torque using the formula: τ = BIA
Relationship between magnetic field, current, and area
Determining the direction of magnetic torque using the right-hand rule
Examples of magnetic torque calculations
Applications of magnetic torque in electric motors and meters

Slide 23: Magnetic Field Due to a Moving Charge

Introduction to magnetic field due to a moving charge
Explanation of the Lorentz force equation: F = qvBsinθ
Calculation of magnetic field using the Lorentz force equation
Relationship between magnetic field, charge velocity, and angle
Examples of magnetic field calculations due to moving charges
Applications of magnetic fields due to moving charges in particle accelerators

Slide 24: Magnetic Fields and Particle Motion

Relationship between magnetic fields and particle motion
Calculation of the radius of a charged particle’s circular path using the formula: r = mv / (qB)
Determining the direction of the particle’s circular motion
Examples of calculations for charged particle motion in magnetic fields
Applications of magnetic fields in particle accelerators and mass spectrometers

Slide 25: Electromagnetic Waves

Introduction to electromagnetic waves
Explanation of the electromagnetic spectrum
Characteristics of electromagnetic waves - wavelength, frequency, and velocity
Relationship between wavelength and frequency using the formula: c = λf
Calculation of wave speed using the formula: c = fλ
Examples of electromagnetic waves and their applications

Slide 26: Electromagnetic Spectrum

Explanation of the different regions of the electromagnetic spectrum
Details of the uses and properties of each region: radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays
Applications of each region in communication, heating, medicine, imaging, etc.
Interactions of electromagnetic waves with matter in various regions
Explanation of how the electromagnetic spectrum is used in astronomy

Slide 27: Electromagnetic Wave Propagation

Explanation of electromagnetic wave propagation
Introduction to the wave equation: v = fλ
Discussion on the speed of light in a vacuum (c)
Explanation of how electromagnetic waves propagate through space
Reflection, refraction, and diffraction of electromagnetic waves
Applications and examples of wave propagation in different mediums

Slide 28: Electromagnetic Induction - Lenz’s Law

Definition and explanation of Lenz’s law
Description of the direction of induced current and magnetic field
Relationship between induced emf, magnetic field, and change in magnetic flux
Application of Lenz’s law in electromagnetic devices
Examples of Lenz’s law in action
Importance of Lenz’s law in electrical engineering and applications

Slide 29: AC Circuits - Introduction

Explanation of AC (alternating current) circuits
Comparison between AC and DC (direct current) circuits
Oscillating voltage and current in AC circuits
Introduction to amplitude, frequency, and phase of an AC wave
Calculation of peak-to-peak voltage and root mean square (RMS) voltage
Examples of AC circuits and their applications

Slide 30: AC Circuits - Impedance

Definition of impedance in AC circuits
Introduction to the different components of impedance: resistance, capacitance, and inductance
Calculation of total impedance in series and parallel AC circuits
Explanation of impedance triangle and phasor diagrams
Examples of calculating impedance in different AC circuits
Applications of impedance in filters and circuit analysis