Estimating the size of a nucleus using electrostatic repulsion can be traced back to the invention of an ultra-sensitive apparatus, which measured forces in terms of the twisting of a fine wire, dating from the 18th Century. This device, known as a torsion balance, is often attributed to the French engineer and physicist Charles Augustin … Continue reading Coulomb’s Law and Nuclear Radii
Exponential changes
Imagine an empty tube train (metro, if you prefer) pulling into a crowded station. When the doors open, people surge forward and the carriage starts to fill very quickly. As the number of people in the carriage increases, the number of remaining spaces decreases and the rate at which further people can board also decreases. … Continue reading Exponential changes
How do electric cells generate a current?
We take for granted the fact that an electric cell (or battery) will cause a current to flow through an external circuit. The current is often discussed in terms of a flow of electrons (like water through a pipe) or energy transferred between adjacent electrons (like a row of dominoes falling onto each other). It … Continue reading How do electric cells generate a current?
Electricity: models and theories
Physics can get complicated at times and when it does, we use models to simplify things. The models aren’t wrong: in fact they work remarkably well, but they aren’t complete. Electricity provides probably the best examples of this state of affairs. Models normally start at the level of “electrons as buckets carrying energy” and include … Continue reading Electricity: models and theories
What are lumens? (part 2)
In the previous discussion about lumens (https://physbang.com/2025/12/30/what-are-lumens/) some numbers were quoted without any explanation. This post adds a bit more detail to those numbers. Firstly, the maximum theoretical output of a light source was stated to be 683 lumens-per-watt. Why that number? The answer is to be found in the definition of the candela, which … Continue reading What are lumens? (part 2)
What are lumens?
Modern light sources are rated in lumens or, more importantly, lumens per watt. The first figure expresses the brightness of the source whereas the second indicates its efficiency. But what, exactly, is a lumen? To answer that question it is useful to recall that the first man-made light sources relied on heat and were very … Continue reading What are lumens?
Charging a Capacitor (analysis)
Changes in charge, current and potential difference during the charging and discharging of a capacitor are all exponential-type behaviours. Specifically, the current that transfers charge to or from a capacitor (during charging or discharging respectively) is always greatest at first and declines to zero as time increases. During discharging, the charge loss and the drop … Continue reading Charging a Capacitor (analysis)
Uncertainties and Error Bars
Measurements are always uncertain: there is no such thing as a perfectly precise measurement. At the very least, the instrument used will limit the precision of the value but in many cases other factors can introduce even greater variability. It is always the greater of these two numbers (the resolution of the instrument and variability … Continue reading Uncertainties and Error Bars
How to determine voltages inside a resistor network
Resistor networks sometimes look scary but they can be solved by taking things one step at a time and applying basic circuit rules. The rules concerned are the calculations for combining series and parallel resistors, together with Kirchoff’s two laws for circuits. To combine resistors, we add their values if they are arranged in series … Continue reading How to determine voltages inside a resistor network
How to Use Logarithms
Although they can seem confusing at first sight, logarithms are just mathematical functions that allow calculations to be carried out quicker than would otherwise be the case. So although they may seen daunting, you should think of logarithms as a way to make calculations easier – once you have mastered the rules. There is quite a … Continue reading How to Use Logarithms
