How to Use a Multimeter to Measure Voltage, Current, and Resistance

© Eugene Brennan

 

What Is a Multimeter?

Multimeters are measurement instruments widely used by professionals in several fields including industrial maintenance and testing, research, appliance repair, and electrical installation. However, a digital multimeter (or DMM) is also an invaluable test instrument for home and DIY use.

Conversations With ChatGPT: Air Drag and Surface Topology

Created by Grok.

Eugene: Is it possible to make a material that has a huge amount of drag that could allow a human to float? And what topology of surface has the most drag, a plane? I know that drag is proportional to cross-sectional area and also that there is a coefficient that depends on the surface shape of an object.

Parabola Equations and Graphs, Directrix and Focus and How to Find Roots of Quadratic Equations

© Eugene Brennan

In this tutorial, you'll learn about a mathematical function called the parabola. We'll cover the definition of the parabola first and how it relates to the solid shape called the cone. Next, we'll explore different ways in which the equation of a parabola can be expressed.

Conversations With ChatGPT: Converting Garden Waste to Electricity

Created by ChatGPT

Eugene: Is it possible to convert the energy stored in garden waste directly into electricity?

Special Relativity and Angle Grinder Disks

© Eugene Brennan

The theory of special relativity was postulated by Einstein in his 1905 paper, "On the Electrodynamics of Moving Bodies". While things behave seemingly "normal" at speeds we experience in our daily lives, bizarre things happen at near-light speeds.

Where Does Water Come From in an Air Compressor Tank?

Graph of temperature versus max water storage capacity of air.

Anyone who owns an air compressor knows that one of the regular maintenance chores is to drain the tank to release water. This is essential to prevent eventual corrosion of the tank.

Rules of Logarithms and Exponents With Worked Examples and Problems

A graph of a log function. Krishnavedala , CC BY-SA 3.0 via Wikimedia Commons

An Introduction to Logarithms, Bases and Exponents

In this tutorial you'll learn about

• exponentiation
• bases
• logarithms to the base 10

Another Use for AI: Reading Tables From Images and Converting to HTML

Screenshot of a table. © Eugene Brennan

Artificial intelligence gets a lot of bad press, so I need to write a proper article at some stage about how beneficial I’ve found it to be for all sorts of tasks.

Summary of Ideal Gas Laws

Thanks to ChatGPT for creating the table to my design. There's a long discussion with ChatGPT about the gas law equations here, where I revise my limited knowledge from school. (which was basically just understanding Boyle's Law and Charles's Law)

Law / Equation	Form / Equation	Derived From	Notes / Conditions
Boyle’s Law	P V = constant	Ideal Gas Law P V = n R T, with T = constant	Isothermal: pressure inversely proportional to volume
Charles’s Law	V / T = constant or V ∝ T	Ideal Gas Law P V = n R T, with P = constant	Isobaric: volume directly proportional to temperature
Gay-Lussac’s Law	P / T = constant or P ∝ T	Ideal Gas Law P V = n R T, with V = constant	Isochoric: pressure directly proportional to temperature
Ideal Gas Law	P V = n R T	Fundamental definition of ideal gases	Connects pressure, volume, temperature, and moles
Combined Gas Law	P V / T = constant P1 V1 / T1 = P2 V2 / T2	Ideal Gas Law, general form combining Boyle, Charles, Gay-Lussac	Relates pressure, volume, and temperature for a fixed amount of gas
Adiabatic PV Relation	P Vγ = constant	First Law dU = -P dV + Ideal Gas Law, γ = Cp/Cv	No heat transfer; pressure rises faster than 1/V
Adiabatic T–V Relation	T Vγ-1 = constant	PV adiabatic relation + Ideal Gas Law	Temperature rises when volume decreases (or vice versa)
Adiabatic T–P Relation	T = constant × P(γ-1)/γ	From PV and T–V adiabatic relations	Temperature as a function of pressure
Adiabatic PV Relation (states)	P1 V1γ = P2 V2γ	PV adiabatic relation applied to two states	Useful for calculating compression/expansion between two points
Adiabatic T–V Relation (states)	T1 V1γ-1 = T2 V2γ-1	T–V adiabatic relation applied to two states	Temperature change for volume change between two states
Adiabatic T–P Relation (states)	T2 = T1 (P2/P1)(γ-1)/γ	T–P adiabatic relation applied to two states	Temperature change for pressure change between two states

Unorthodox Fire Starting Devices

A fire plunger. Image courtesy eBay

Two gadgets for those who need to light a fire when camping or otherwise and want to show off (although a cigarette or gas lighter is perfectly adequate):

How to Understand Calculus: Integration Rules and Examples

© Eugene Brennan

What Is Calculus?

Calculus is a study of rates of change of functions and accumulation of infinitesimally small quantities. It can be broadly divided into two branches:

What Is Calculus? A Beginner's Guide to Limits and Differentiation

 © Eugene Brennan

Calculus is a study of rates of change of functions and accumulation of infinitesimally small quantities. It can be broadly divided into two branches:

• Differential Calculus. This concerns rates of changes of quantities and slopes of curves or surfaces in 2D or multidimensional space.
• Integral Calculus. This involves summing infinitesimally small quantities.

What Would Happen if You Fell Down a Hole That Went Through the Centre of the Earth?

Created by Grok

Well you'd be incinerated as you pass through the hot and molten core! But imagine if the core wasn't there or you had a special suit that protected you from the heat—what would happen then? Would you suddenly stop when you got to Oz?