Q: A blacksmith splits open a doughnut-shaped torus as pictured below: The inner radius of the torus is 1.75 cm, and the outside radius is 2.25 cm. If the torus is made of low-carbon steel, what is its reluctance? A: Let’s begin by viewing the torus from above prior to being split apart: The threeContinue reading “INTRODUCTION TO ELECTRONICS: Reluctance and Permeability of Magnetic Materials”
Category Archives: Mathematics
INTRODUCTION TO ELECTRONICS: Permeability and Reluctance of Magnetic Materials
Many uncanny comparisons can be made between the behavior of electric currents and magnetic flux ( ϕ ) within conductive materials. In the same way that some materials conduct current better than others, metallic materials differentially provide pathways through which magnetic flux can permeate. The permeability ( μ ) of any material is relative toContinue reading “INTRODUCTION TO ELECTRONICS: Permeability and Reluctance of Magnetic Materials”
INTRODUCTION TO ELECTRONICS: Permanent Magnets, Contact Switches, and Hall Effect Sensors
Prior to engaging in studies of electromagnetic devices, an examination of simple yet very important devices made of permanent magnets is due. In the diagram below, a magnet is used to control a switch that regulates the flow of electricity in a circuit: In order to close the circuit and elicit flow of electric currentContinue reading “INTRODUCTION TO ELECTRONICS: Permanent Magnets, Contact Switches, and Hall Effect Sensors“
INTRODUCTION TO ELECTRONICS: Magnetic Flux Density
Magnetic field lines represent regions of space that have the ability to enact forces upon charged particles in motion. Likewise, a stationary charged particle will experience a force from a nearby magnet when it is put into motion. Time and time again, we will see that the magnitude of the force enacted by a magneticContinue reading “INTRODUCTION TO ELECTRONICS: Magnetic Flux Density“
INTRODUCTION TO ELECTRONICS: Magnetism and the Magnetic Field
The concept of “ free space “ may be visually appealing to the senses, but this perception very rarely ( if ever ) describes any meaningful description of any region of space. This argument can easily be confirmed with objects as simple as paper clips and refrigerator magnets. Under the right conditions, seemingly magical forcesContinue reading “INTRODUCTION TO ELECTRONICS: Magnetism and the Magnetic Field“
INTRODUCTION TO ELECTRONICS: The Superposition Theorem
Q: What is the total current ( IT ) and voltage ( V3 ) across resistor R3? A: In order to begin evaluating the circuit from the vantage point of Vs1, we place a short across Vs2 : Within this circuit, negatively charged electrons move upward and across the R3 resistor towards the positively chargedContinue reading “INTRODUCTION TO ELECTRONICS: The Superposition Theorem“
INTRODUCTION TO ELECTRONICS: The Superposition Theorem
Q: How much current flows across R2? What is the voltage drop across R2? A: We begin by evaluating the circuit from two points of view: Vs1 and Vs2. In order to begin our journey, the Vs2 voltage source is shorted: From the vantage point of Vs1, resistor R1 is in series with resistors R2Continue reading “INTRODUCTION TO ELECTRONICS: The Superposition Theorem“
INTRODUCTION TO ELECTRONICS: The Superposition Theorem
Most of the circuits we’ve encountered thus far contain a single voltage ( V ) source that provides current ( I ) to the system. Suppose, however, that a current determination must be made for the following dual-voltage circuit type: The presence of two voltage sources eliminates any series-parallel relationships that would exist between theContinue reading “INTRODUCTION TO ELECTRONICS: The Superposition Theorem“
INTRODUCTION TO ELECTRONICS: The Maximum Power Transfer Theorem
Within the field of electronics, a delicate balance between energy transfer and efficiency must be maintained; however, in some circumstances, maximum power ( P ) must be delivered to a load without regard to how inefficient the process may be. Herein lies the concept of maximum power transfer. The mathematical derivations relevant to this processContinue reading “INTRODUCTION TO ELECTRONICS: The Maximum Power Transfer Theorem“
INTRODUCTION TO ELECTRONICS: Wheatstone Bridge Voltage and Current Determination
A Wheatstone bridge circuit has the following voltage ( Vs ) and resistor ( R ) values: Q: What is the value for the voltage ( VL ) drop and current ( I ) across the load resistor ( RL )? A: We begin by removing the load resistor and marking the new terminals ofContinue reading “INTRODUCTION TO ELECTRONICS: Wheatstone Bridge Voltage and Current Determination“
RENAISSANCE PHYSICS 